Dissertations / Theses on the topic 'EDP non linéaires [Équations aux dérivées partielles]'
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Khenissy, Saïma. "Équations aux dérivées partielles elliptiques non linéaires : équation de Ginzburg-Landau : équation de Bahri-Coron sur-critique." Paris 6, 2002. http://www.theses.fr/2002PA066197.
Full textYazidi, Habib. "Étude de quelques EDP non linéaires sans compacité." Paris 12, 2006. https://athena.u-pec.fr/primo-explore/search?query=any,exact,990002325100204611&vid=upec.
Full textThis thesis is devoted to the study of some nonlinear partial differential equations of Dirichelet or Neumann type, with a non compact variational structure. In the first part, we study homogeneous PDE with a positive weight, with the critical Sobolev exponent and a parameter λ. We establish some existence and non-existence results which depend on the behavior of the weight near its minima, the parameter λ and the geometry of the domain. In the second part, we are interseted by some non-homogeneous PDE with weight and with a critical nonlinearity on the boundary. We show some existence results which depend on the various coefficients of the studied PDE, and of the mean curvature of the boundary of the domain
Huang, Guan. "Une théorie de la moyenne pour les équations aux dérivées partielles non linéaires." Phd thesis, Ecole Polytechnique X, 2014. http://pastel.archives-ouvertes.fr/pastel-01002527.
Full textFahim, Arash. "Une Méthode Numérique Probabiliste pour les Équations aux Dérivées Partielles Paraboliques et complètement non-linéaires." Phd thesis, Ecole Polytechnique X, 2010. http://tel.archives-ouvertes.fr/tel-00540175.
Full textAydi, Hassen. "Vorticité dans le modèle de Ginzburg-Landau de la supraconductivité." Phd thesis, Université Paris XII Val de Marne, 2004. http://tel.archives-ouvertes.fr/tel-00297136.
Full textEn première partie, on prouve pour des certeins champs magnétiques appliqués $h_{ex}$ à la surface du supraconducteur de l'ordre du premier champ critique $H_{c_1}=\frac{|\log\e|}{2}$ que pour les minimiseurs périodiques de Ginzburg-Landau, le nombre des vortex par période est de l'ordre de $h_{ex}$ et leur répartition est uniforme. En outre, en prenant des champs $h_{ex}$ proches de $H_{c_1}$ de la forme $h_{ex}=H_{c_1}+f(\e)$ où $f(\e)\rightarrow +\infty$ et $f(\e)=o(|\log\e|)$, on montre que le nombre de vortex des minimiseurs périodiques par période est de l'ordre de $f(\e)$ et leur répartition est aussi uniforme.
Dans une deuxième partie, toujours dans le modèle périodique, on construit une suite de points critiques ayant des vortex répartis sur un nombre fini de lignes horizontales.
Dans une troisième partie, on construit dans le cas d'un disque une suite de points critiques telle que les vortex sont répartis sur un nombre fini de cercles concentriques de rayon strictement positif et de centre, le centre du disque. Dans le cas où il y a un seul cercle de vorticité, le rayon est bien caractérisé.
Finalement, dans un modèle de Ginzburg-Landau avec "pinning", on s'intéresse à l'étude du signe des degrés des vortex et on donne des résultats partiels indiquant que les degrés ne sont pas toujours positifs.
Ntovoris, Eleftherios. "Contribution à la théorie des EDP non linéaires avec applications à la méthode des surfaces de niveau, aux fluides non newtoniens et à l'équation de Boltzmann." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1057/document.
Full textThis thesis consists of three different and independent chapters, concerning the mathematical study of three distinctive physical problems, which are modelled by three non- linear partial differential equations. These equations concern the level set method, the theory of incompressible flow of non-Newtonian materials and the kinetic theory of rare- fied gases. The first chapter of the thesis concerns the dynamics of moving interfaces and contains a rigorous justification of a numerical procedure called re-initialization, for which there are several applications in the context of the level set method. We apply these results for first order level set equations. We write the re-initialization procedure as a splitting algorithm and study the convergence of the algorithm using homogenization techniques in the time variable. As a result of the rigorous analysis, we are also able to introduce a new method for the approximation of the distance function in the context of the level set method. In the case where one only looks for a level set function with gradient bounded from below near the zero level, we propose a simpler approximation. In the general case where the zero level might present changes of topology we introduce a new notion of relaxed limits. In the second chapter of the thesis, we study a free boundary problem arising in the study of the flow of an incompressible non-Newtonian material with Drucker-Prager plasticity on an inclined plane. We derive a subdifferential equation, which we reformulate as a variational problem containing a term with linear growth in the gradient variable, and we study the problem in an unbounded domain. We show that the equations are well posed and satisfy some regularity properties. We are then able to connect the physical parameters with the abstract problem and prove some quantitative properties of the solution. In particular, we show that the solution has compact support and the support is the free boundary. We also construct explicit solutions of an ordinary differential equation, which we use to estimate the free boundary. The last chapter of the thesis is dedicated to the study of infinite energy solutions of the homogeneous Boltzmann equation with Maxwellian molecules. We obtain new results concerning the existence of eternal solutions in the space of probability measure with infinite energy (i.e. the second order moment is infinite). These solutions describe the asymptotic behaviour of other infinite energy solutions but could also be useful in the study of intermediate asymptotic states of solutions with finite but arbitrarily large energy. We use harmonic analysis tools to study the equation, where the velocity variable is expressed in the Fourier space. Finally, a logarithmic scaling of the time variable allows to determine the correct asymptotic scaling of the solutions
Guelmame, Billel. "Sur une régularisation hamiltonienne et la régularité des solutions entropiques de certaines équations hyperboliques non linéaires." Thesis, Université Côte d'Azur, 2020. https://tel.archives-ouvertes.fr/tel-03177654.
Full textIn this thesis, we study some non-dispersive conservative regularisations for the scalar conservation laws and also for the barotropic Euler system. Those regularisations are obtained inspired by a regularised Saint-Venant system introduced by Clamond and Dutykh in 2017. We also study the regularity, in generalised BV spaces, of the entropy solutions of some nonlinear hyperbolic equations. In the first part, we obtain and study a suitable regularisation of the inviscid Burgers equation, as well as its generalisation to scalar conservation laws. We prove that this regularisation is locally well-posedness for smooth solutions. We also prove the global existence of solutions that satisfy a one-sided Oleinik inequality for uniformly convex fluxes. When the regularising parameter ``l’’ goes to zero, we prove that the solutions converge, up to a subsequence, to the solutions of the original scalar conservation law, at least for a short time. We also generalise the regularised Saint-Venant equations to obtain a regularisation of the barotropic Euler system, and the Saint-Venant system with uneven bottom. We prove that both systems are locally well-posed in Hs, with s ≥ 2. In the second part, we prove a regularising effect, on the initial data, of scalar conservation laws with Lipschitz strictly convex flux, and of scalar equations with a linear source term. For some cases, we give a limit of the regularising effect.Finally, we prove the global existence of entropy solutions of a class of triangular systems involving a transport equation in BV^s x L^∞ where s > 1/3
Luçon, Eric. "Oscillateurs couplés, désordre et synchronisation." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00709998.
Full textXu, Chao-Jiang. "Équations aux dérivées partielles non linéaires sous-elliptiques." Paris 11, 1986. http://www.theses.fr/1986PA112016.
Full textIn a first part, we prove a regularity theorem for solution of non-linear partial differential equation of second order: if u is a smooth enough real solution, if the principal symbol of the linearized operator is positive, and if the Hörmander's or Oleinik- Radkevič 's condition is satisfied, then […]. With similar methods, we prove that: if […] is a "very strict" minimum of an integral functional […], i. E. If for all x in Ω, there are a neighborhood K of x , C > 0 , Ɛ > 0 , such as […] for all […], then […]. In a second part, we consider partial differential equation of form […] where X₁,…,Xᵨ are vectors fields satisfying Hörmander' s condition. Let us u be of smooth enough solution, we suppose that the localization of the linearized operator on the Lie group associated to the system of the […] is hypoelliptic, we prove with this hypothesis that […]. In a third part, we study some linear differential operators of second order 2 with C² - coefficients, these operators satisfying the Fefferman-Phong geometric condition; we prove they are sub-elliptic on R² and we so obtain a regularity theorem for nonlinear problems
Normand, Raoul. "Modèles déterministes et aléatoires d'agrégation limitée et phénomène de gélification." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2011. http://tel.archives-ouvertes.fr/tel-00631419.
Full textSellami-Omrani, Sonia. "Equations aux dérivées partielles non-linéaires et ondes progressives." Paris 6, 1993. http://www.theses.fr/1993PA066641.
Full textNabaji, Abdellah. "Solutions ramifiées d'équations aux dérivées partielles non linéaires." Toulouse 3, 1993. http://www.theses.fr/1993TOU30023.
Full textLaurent, Camille. "Contrôle d’équations aux dérivées partielles non linéaires dispersives." Paris 11, 2010. http://www.theses.fr/2010PA112119.
Full textIn this thesis, we study the controllability and the stabilization of some dispersive partial differential equations. We are first interested in the internal control. Thanks to some microlocal analysis methods and the use of Bourgain spaces, we prove stabilization and control in large time for the non linear Schrödinger equation on an interval and then on some manifolds of dimension 3. Moreover, we prove the controllability near trajectories, from which we deduce a second proof of global controllability. We then apply these methods to the Korteweg-de Vries equation on a periodic domain. We also study the Klein Gordon equation with a critical nonlinearity on some compact manifolds. Under some assumptions slightly stronger than the geometric control condition, we prove the stabilization and controllability in large time for high frequency data. The proof requires the statement of a profile decomposition on manifolds for which some geometric effects have to be analysed. In a last part, we study the bilinear control. Thanks to a regularizing effect, we establish the local controllability of the Schrödinger equation on an interval with a proof simpler than in the available litterature, allowing to reach the optimal spaces and in an arbitrary time. The method is robust enough to be extended to other situations: radial data on a ball, non linear Schrödinger equation and non linear wave equation on an interval
Laurent, Camille. "Contrôle d'équations aux dérivées partielles non linéaires dispersives." Phd thesis, Université Paris Sud - Paris XI, 2010. http://tel.archives-ouvertes.fr/tel-00536082.
Full textBartier, Jean-Philippe. "Méthode d'entropie et comportement asymptotique des solutions d'équations paraboliques linéaires et non-linéaires." Paris 9, 2005. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2005PA090070.
Full textGiletti, Thomas. "Phénomènes de propagation dans des milieux diffusifs excitables : vitesses d'expansion et systèmes avec pertes." Thesis, Aix-Marseille 3, 2011. http://www.theses.fr/2011AIX30043.
Full textReaction-diffusion systems arise in the description of phase transitions in various fields of natural sciences. This thesis is concerned with the mathematical analysis of propagation models in some diffusive, unbounded and heterogeneous media, which comes within the scope of an active research subject. The first part deals with the single equation, by looking at the inside structure of fronts, or by exhibiting new dynamics where the profile of propagation may not have a unique speed. In a second part, we take interest in some systems of two equations, where the lack of maximum principles raises many theoretical issues. Those works aim to provide a better understanding of the underlying processes of propagation phenomena. They highlight new features for reaction-diffusion problems, some of them not known before, and hence help to improve the theoretical approach as an alternative to empirical analysis
Bernardi, Christine. "Contribution à l'analyse numérique de problèmes non linéaires." Paris 6, 1986. http://www.theses.fr/1986PA066387.
Full textLeboucher, Guillaume. "Méthodes de moyennisation stroboscopique appliquées aux équations aux dérivées partielles hautement oscillantes." Thesis, Rennes 1, 2015. http://www.theses.fr/2015REN1S121/document.
Full textThis thesis presents some original work in the field of high order averaging procedure. In particular, we are interested in stroboscopic and quasi-stroboscopic averaging procedure in abstract Banach or Hilbert spaces. This procedures is applied to concrete examples: some highly oscillatory evolution equations. More precisely, we first show a theorem of stroboscopic averaging in a Banach space where we obtain exponential error estimates. This theorem is then applied on two semi-linear and highly oscillatory wave equations. We also put in evidence that the {\it Stroboscopic Averaging Method} works fine with a semi-linear wave equation with Dirichlet conditions. Finally, the averaging procedure puts in evidence, numerically, an interesting dynamics regarding the semi-linear wave equation with Dirichlet conditions. In a second part, we present a quasi-stroboscopic averaging theorem in a Hilbert space with exponential error estimates. This theorem is applied on a semi-linear Schrödinger equation. This equation has first, to be project in a finite dimensional space in order to fit in the hypotheses of the theorem. We then write a quasi-stroboscopic averaging theorem for a semi-linear Schrödinger equation with polynomial error estimates
Jourdain, Benjamin. "Sur l'interprétation probabiliste de quelques équations aux dérivées partielles non linéaires." Phd thesis, Ecole des Ponts ParisTech, 1998. http://tel.archives-ouvertes.fr/tel-00005616.
Full textThirouin, Joseph. "Instabilité et croissance des normes de Sobolev pour certaines EDP hamiltoniennes." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS195/document.
Full textIn this thesis we study global smooth solutions of certain Hamiltonian PDEs, in order to capture the possible growth of their Sobolev norms. Such a phenomenon is typical for what is sometimes called "weak turbulence" : a change in the distribution of energy between Fourier modes. We first study a nonlinear evolution equation involving a fractional Laplacian, and we prove a priori estimates on the growth of Sobolev norms. We then introduce an equation where these estimates turn out to be optimal : an integrable Szegő equation with a quadratic nonlinearity, which admits exponentially growing smooth solutions that remain bounded in the energy space. We classify the traveling wave solutions of this quadratic Szegő equation, and show that some of them are unstable. Eventually we find a hierarchy of conservation laws for this equation, which leads us into a deeper study of rational turbulent solutions
Wantz, Mézières Sophie. "Etude de processus stochastiques non linéaires." Nancy 1, 1997. http://docnum.univ-lorraine.fr/public/SCD_T_1997_0163_WANTZ_MEZIERES.pdf.
Full textOur study deals with processes which are solutions of stochastic differential equations in which the law of the solution can interact. We etablish an instability phenomena for a two-dimensional stochastic process which density verifies a P. D. E. Of Burgers' type: the solution fluctuates when the diffusion tends to zero. For an ordinary S. D. E with inward drift, we study the asymptotic behaviour of hitting times for the process to a fixed point when the starting point goes to infinity. We consider another equation with inward drift which is more non linear and reflected in a real interval and we prove that the process tends in law to a unique stationnary measure. We solve a simulation problem for a two-dimensional stochastic process composed of a one-dimensional process and an integral related to this process
Duminil, Sébastien. "Extrapolation vectorielle et applications aux équations aux dérivées partielles." Phd thesis, Université du Littoral Côte d'Opale, 2012. http://tel.archives-ouvertes.fr/tel-00790115.
Full textSalazar, Wilfredo. "Contribution aux équations aux dérivées partielles non linéaires et non locales et application au trafic routier." Thesis, Rouen, INSA, 2016. http://www.theses.fr/2016ISAM0016/document.
Full textThis work deals with the modelling, analysis and numerical analysis of non- linear and non-local partial differential equations and their application to traffic flow. Traffic can be simulated at different scales. Mainly, we have the microscopic scale which describes the dynamics of each of the vehicles individually and the macroscopic scale which describes the traffic as a fluid using macroscopic quantities such as the density of vehicles and the average speed. In this PhD thesis, using the theory of viscosity solutions, we derive macroscopic models from microscopic models. The interest of these results is that microscopic models are very intuitive and easy to manipulate to describe a particular situation (bifurcation, a traffic light,...), however, they are not adapted for big simulations (to simulate the traffic in an entire city for example). Conversely, macroscopic models are less easy to modify (to simulate a particular situation) but they can be used for big simulations. The idea is then to find the macroscopic model equivalent to a microscopic model describing a particular scenario (a junction, a bifurcation, different types of drivers, a school zone,...). The first part of this work contains an homogenization result and a numerical homogenization result for a microscopic model with different types of drivers. The second part contains an homogenization and numerical homogenization result for microscopic models with a local perturbation (a moderator, a school zone,...). Finally, we present an homogenization result for a bifurcation
Boussaid, Nabile. "Etude de la stabilité des petites solutions stationnaires pour une classe d'équations de Dirac non linéaires." Paris 9, 2006. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2006PA090012.
Full textThis thesis is devoted to the study of the stability of small stationary solutions of a nonlinear time dependent equation coming from relativistic quantum mechanics: the nonlinear Dirac equation. In this study, non linear equations are viewed as small nonlinear perturbations of linear systems. A part of this thesis is hence devoted to the study of linear problems. We prove that for a Dirac operator, with no resonance at thresholds nor eigenvalue at thresholds, the propagator satisfies propagation and dispersive estimates. We also deduce smoothness estimates in the sense of Kato and Strichartz estimates. With some ad hoc assumptions on the discrete spectrum of a Dirac operator, we build small manifolds of stationary states. Then with small variations on these assumptions, we can highlight some stabilization process and orbital instability phenomena for some stationary states
Antonini, Christophe. "Etude qualitative de la formation des singularités pour certaines équations aux dérivées partielles non linéaires." Cergy-Pontoise, 2001. http://biblioweb.u-cergy.fr/theses/01CERG0136.pdf.
Full textIn this thesis, I study two nonlinear evolution partial differential equations whose solutions may blow-up in finite time. In the first part, I consider the nonlinear Schrödinger equation with critical exponent in the space periodic case and obtain a lower bound for the blow-up rate under the condition of minimal mass. In parts 2 and 3, I study a semi-linear wave equation. In part 2 we obtain optimal bounds on the blow-up rate, and in part 3 I study the asymptotic behaviour to solutions of this equation
Colombeau, Mathilde. "Une étude mathématique des équations aux dérivées partielles non linéaires présentant des solutions irrégulières." Thesis, Antilles-Guyane, 2011. http://www.theses.fr/2011AGUY0478/document.
Full textThis thesis is devoted to the theoretical and numerical study of singular solutions appearing in nonlinear partial differential complicates the mathematical understanding of the phenomena under concem as well as their numerical treatment, in particular in view of computation. These equations are studied by a regularization method in an appropriate functional space. When completely different numerical methods give the same results up to the smallest details one can reasonably expect that these numerical results suggest the existence of a mathematical solution of theses equations. We construct sequences of approximate solutions from an original numerical scheme, which is stable and simple enough to prove that these sequences constitute a Maslov asymptotic method in three space dimension. The regularization technique in use consits in extending the real variables of the problem into complex ones, which perrnits to construct families of particular equations that we bring back to the real case by letting a small paramater tend to zero. The expected physical solutions appear as boundary values of holomorphie functions . Illustrations are given by applications to cosmology in the Newtorian and re1ativistic settings for pressure1ess fluid dynamics, then in presence of self-gravitation and pressure as weil as for the systemof ideal gases
Baraket, Sami. "Quelques résultats sur des équations aux dérivées partielles non linéaires provenant de problèmes géométriques." Cachan, Ecole normale supérieure, 1994. http://www.theses.fr/1994DENS0012.
Full textLeichtnam, Éric. "Contributions à l'étude des singularités des solutions des équations aux dérivées partielles non linéaires." Paris 11, 1987. http://www.theses.fr/1987PA112106.
Full textThis work falls into four papers. In the first one, we define in an intrinsic way the wave front set of a submanifold the regularity of which is limited. Then we use this concept to study the microlocal singularities of solutions of partial differential equations in several situations: equations of the first order, Monge-Ampère equations, Pfaffian systems. In the second paper, we study the interaction of singularities for a pseudo differential operator with a real principal symbol and the characteristic variety of which is the union of two smooth hypersurfaces with non involutive self-intersection. In the third article, we construct for a holomorphic quasilinear operator solutions which are ramified around a smooth complex characteristic hypersurface. In the fourth paper, we study the microlocal regularity of the solutions of nonlinear non characteristic Dirichlet problems of the second order and with a non-smooth boundary
Pacard, Frank. "Existence et compacité de solutions de certaines équations aux dérivées partielles elliptiques non-linéaires." Paris 11, 1991. http://www.theses.fr/1991PA112151.
Full textImekraz, Rafik. "Etude dynamique de quelques équations aux dérivées partielles hamiltoniennes non linéaires à potentiel confinant." Nantes, 2010. http://archive.bu.univ-nantes.fr/pollux/show.action?id=f78473aa-7d4c-4a95-a2c8-e6d600ac58cd.
Full textThis thesis is concerned by stability of solutions of some non linear Schroedinger partial differential equations (PDE) on Rn with a confining potential and a regular initial condition. Two potentials are studied : the harmonic oscillator multidimensional and the polynomial confining potential unidimensional. In our context, the stability means roughly the following : the solution exists on a time-interval whose length depends polynomially on the smallness of the initial condition (almost global existence) and stays near the solution of an explicit completely integrable equation with the same initial condition. We use the Birkhoff's normal forms theory to handle our issue. The key point is the Hamiltonian structure of our PDE. We create an abstract differential model (which encompasses our PDE) and prove that it has a Birkhoff's normal form of all order, ie a proper renormalization of the Hamiltonian which ensures in particular the stability
Bigorgne, Léo. "Propriétés asymptotiques des solutions à données petites du système de Vlasov-Maxwell." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS164/document.
Full textThe purpose of this thesis is to study the asymptotic properties of the small data solutions of the Vlasov-Maxwell system using vector field methods for both the electromagnetic field and the particle density. No compact support asumption is required on the initial data. Instead, we make crucial use of the null structure of the equations in order to deal with a resonant phenomenon caused by the particles approaching the speed of propagation of the Maxwell equations. Due to the robustness of vector field methods and contrary to previous works on this topic, we also study plasmas with massless particles.We start by investigating the high dimensional cases d ≥ 4 where dispersive effects allow us to derive strong decay rate on the solutions of the system and their derivatives. For that purpose, we proved a new decay estimate for solutions to massive relativistic transport equations. In order to obtain an analogous result for massless particles, we required the velocity support of the distribution function to be initially bounded away from $0$ and we then proved that this assumption is actually necessary. The second part of this thesis is devoted to the three dimensional massless case, where a stronger understanding of the null structure of the Vlasov-Maxwell system is essential in order to derive the optimal decay rate of the null components of the electromagnetic field, the velocity average of the particle density and their derivatives. We then focus on the asymptotic behavior of the small data solutions of the massive Vlasov-Maxwell system in 3d. Specific problems force us to modify the vector fields used previously to study the Vlasov field in order to compensate the worst error terms in the commuted transport equations. Finally, still for the massive system in 3d, we restrict our study of the solutions to the exterior of a light cone. The strong decay properties satisfied by the velocity average of the particle density in such a region permit us to relax the hypothesis on the initial data and lead to a much simpler proof
El, Mufti Karim. "Presque-périodicité et quasi-périodicité des solutions de certains systèmes d'évolution non linéaires non autonomes." Paris 9, 1999. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1999PA090055.
Full textScotti, Simone. "Applications of the error theory using Dirichlet forms." Phd thesis, Université Paris-Est, 2008. http://tel.archives-ouvertes.fr/tel-00349241.
Full textKhayamian, Chiara. "Periodic and Quasi-Periodic Solutions of some Non-Linear Hamiltonian PDE's." Thesis, Avignon, 2017. http://www.theses.fr/2017AVIG0418/document.
Full textThe aim of this thesis is the research of periodic and quasi-periodic solutions for some non-linear hamiltonian PDEs
Jouannelle, Olivier. "Une étude comparative entre des schémas numériques 2D et splitting pour des e. D. P hyperboliques non linéaires bidimensionnelles dans le cadre des fonctions généralisées." Antilles-Guyane, 2010. https://hal.archives-ouvertes.fr/tel-01487366.
Full textThis work is devoted to the theoritical research and to the numerical calculus of weak solutions (in the sens of generalized functions) for the non linear transport equation8u 8f(u) 8g(u)8t (x,y,t) +a(x,y,t)-ax(x,y,t) +b(x,y,t)fiij(x,y,t) = °pour t > 0with the initial condition u(x, y, 0) = uo(x, y) where the functions {(x, y, t) --;. A(x, y, tn and {(x, y, t) --;. B(x, y, tn belong to L00 (R2 X R+) (but can be discontinuous), the functions f and g are smooth and monotonous, the function ((x,y) --;. Uo(x,yn belongs to Loo(JR2). We recall the necessary notions on nonlinear generalized functions for introducing their tensorial product. The main results (to determine the weak solutions) are sufficient conditions so that, when a sum of generalized functions (like Heaviside or Dirac products) is associated with zero, each terms of the sum is equal to zero. Thanks to these theoretical results, we can solve the Riemann problem with the help of a solver written like tensorial product of Heaviside functions (or like a sum of tensorial product of Heaviside functions) in order to obtain the weak solutions. These weak solutions allow to develop two dimensional numerical Godunov type schemes. Then, numerical tests are performed which give a comparison between the results obtained by these 2D schemes and the ones of the splitting method. These tests prove that the 2D numerical schemes are as reliable as the ones obtained by splitting. They are also more simple in their expression. Moreover, a more detailed comparative study of the two types of numerical schemes show that the 2D schemes are far less expensive in the linear case as well as in the non linear case. They are stable for the LOO norm, unlike the splitting schemes
Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150/document.
Full textThe main concern of this thesis deals with the study of solutions of several elliptic partial differential equations via the Morse index, including the stable solutions, i.e. when the Morse index is zero. The thesis has two independent parts. In the first part, under suplinear and subcritical assumptions on f, we establish firstly some explicit estimation for the L1 norms of solutions to -Δu = f(u) avec u = 0 on the boundary, via its Morse index. We propose an approach more transparent and easier than the work of Yang [1998], which allow us to treat some nonlinearities very close to the critical growth. These results motivated us to consider the polyharmonic equations (-Δ)ku = f(x; u) with especially k = 2 and 3. With the hypothesis on f similar to Yang [1998] and appropriate boundary conditions, we obtain for the _rst time some explicit estimations of solution via its Morse index, for the polyharmonic equations.In the second part, we consider a Lane-Emden system -Δu = ρ(x)vp; -Δv = ρ(x)u_; u; v > 0; in RN; with 1 < p< θ and a radial positive weight ρ. We prove the non-existence of stable solution in small dimension case. Our results improve the previous works Cowan & Fazly [2012]; Fazly [2012]; Hu [2015], especially we prove some general Liouville type results for stable solutions in small dimension which hold true for any 1 < ρ min(4 3 ; θ)
Chemin, Jean-Yves. "Théorèmes de régularité pour les solutions d'équations aux dérivées partielles non linéaires hyperboliques." Paris 11, 1987. http://www.theses.fr/1987PA112009.
Full textIn the thesis, we prove theorems of regularity for solutions of non linear strictly hyperbolic equations in the three following situations :. In the case of dimension two, we prove a theorem describing the regularity of solutions in relation to what we know on a line t = t0, and on the geometry of characteristics in any dimension, we emphasize a phenomenon of controled interaction for singularities going up to three times the global regularity of the solution. In dimension three, we prove a theorem describing the interaction of three progressing waves for semi-linear equations of order two
Royer, Manuela. "Équations différentielles stochastiques rétrogrades et martingales non linéaires." Rennes 1, 2003. http://www.theses.fr/2003REN1A018.
Full textPerrollaz, Vincent. "Problèmes de contrôle et équations hyperboliques non-linéaires." Paris 6, 2011. http://www.theses.fr/2011PA066551.
Full textBiton, Samuel. "Semi-groupes monotones non-linéaires, équations géométriques et solutions de viscosité des équations quasilinéaires paraboliques." Tours, 2001. http://www.theses.fr/2001TOUR4028.
Full textIn the first part of this thesis we show that any monotone semi-group defined on continuous functions and satisfying suitable assumptions of regularity and locality is a semi-group associated to a second order parabolic pde. In a second part, we study uniqueness and existence properties of the solutions of the mean curvature equation for graphs and also for sme related class àf quasilinear parabolic equations. In a first article, we use the "level set approach" which provides a L[infini] local bound and a formulation of the uniqueness problem in term of fattening of the 0-level set of an auxiliary function. The major application of the method is a complete result of existence and uniqueness for a class of quasilinear equations without restriction on the behavior at infinity when the initial graphs is convex. In a second article, we prove the uniqueness result for the mean curvature flow of graphs in the one dimensional case without growth condition at infinity for the solution or the initial graph. Finally, in the third paper, we prove a comparison result in dimension N in the class of functions with polynomial growth. This result is obtained under growth conditions of polynomial type on the grandients of the initial data
Ye, Dong. "Sur quelques équations aux dérivées partielles non linéaires provenant de la géométrie et de la physique." Cachan, Ecole normale supérieure, 1994. http://www.theses.fr/1994DENS0005.
Full textChaïb, Karim. "Quelques résultats sur les systèmes d'équations aux dérivées partielles faisant intervenir l'opérateur p-Laplacien." Toulouse 3, 2002. http://www.theses.fr/2002TOU30028.
Full textEsteban, Galarza Maria Jesus. "Etude de quelques problèmes variationnels et équations aux dérivées partielles non linéaires de la Physique mathématique." Paris 6, 1987. http://www.theses.fr/1987PA066126.
Full textBenmohamed, Abdelkader. "Espaces de Besov et propagation des singularités des solutions non bornées, d'équations aux dérivées partielles non-linéaires." Paris 11, 1987. http://www.theses.fr/1987PA112509.
Full textThis thesis is devoted to the study of the propagation of microlocal singularities for some (locally) unbounded solutions of non-linear partial differential equations. These solutions are assumed in a Besov space. We begin by studying the behaviour of the composition map F (u) where u is locally in Besov space which is not an algebra and F is in some reasonable class of functions ; so we obtain that F(u) is locally in another Besov space. Then, we develop a symbolic calculus for paradifferential operators whose symbols are unbounded. This will allows us to linearize non-linear equations in the sens of BONY and then, to prove some results on the propagation of microlocal Sobolev-singularities for unbounded solutions of non-linear partial differential equations
Rouquès, Jean-Philippe. "Asymptotique de Laplace pour l'équation de KPP généralisée." Paris 9, 1995. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1995PA090013.
Full textWe obtain precise asymptotics of the solution of one dimensional, non homogeneous with small parameter KPP equation (nonlinear heat equation) for points ahead of the Freidlin-KPP front. The proff is probabilistic, and uses Feynman-Kac formula and large deviations technics
Lissy, Pierre. "Sur la contrôlabilité et son coût pour quelques équations aux dérivées partielles." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00918763.
Full textGautier, Éric. "Grandes déviations pour les équations de Schrödinger non linéaires stochastiques et applications." Rennes 1, 2005. https://pastel.archives-ouvertes.fr/tel-00011274.
Full textAzerad, Pascal. "Contributions à l'étude de quelques équations aux dérivées partielles, en mécanique des fluides et en génie côtier." Habilitation à diriger des recherches, Université Montpellier II - Sciences et Techniques du Languedoc, 2007. http://tel.archives-ouvertes.fr/tel-00221442.
Full textIls se classent en trois thèmes:
Analyse asymptotique des équations de Navier-Stokes,
Optimisation de forme d'ouvrages de lutte contre l'érosion du littoral,
Etude d'équations aux dérivées partielles comportant des termes non-locaux.
Dans le thème 1, je développe la justification mathématique de l'approximation hydrostatique pour les fluides géophysiques à faible quotient d'aspect, hypothèse couramment vérifiée en océanographie et en météorologie. C'est un problème de perturbation singulière. Je présente également l'étude théorique et numérique de l'écoulement cône-plan, utilisé en hématologie-hémostase pour le sang de patients. Il s'agit d'un problème de couche limite singulière.
Le thème 2 concerne le génie côtier. Les ouvrages utilisés tels que épis, brise-lames, enrochements sont de forme trop rudimentaire. Leur efficacité peut être améliorée significativement si leur forme est optimisée pour réduire l'énergie dissipée par la houle dans la zone proche-littorale. Nous optimisons aussi la forme de géotextiles immergés. Ce travail, réalisé dans le cadre de la thèse de Damien Isèbe, a reçu le soutien de l'ANR (projet COPTER) et s'effectue en partenariat avec le laboratoire Géosciences Montpellier et l'entreprise Bas-Rhône-Languedoc ingénierie (Nîmes).
Dans le thème 3, nous prouvons existence, unicité et régularité de solutions pour l'équation de la chaleur fractionnaire, perturbée par un bruit blanc. C'est une équation aux dérivées partielles stochastique.Nous prouvons enfin un résultat d'existence, unicité et dépendance continue pour une loi de conservation non linéaire, comportant un terme non local, qui modélise l'évolution d'un profil de dune immergée.
L'intérêt mathématique est que l'équation ne vérifie pas le principe du maximum mais possède néanmoins un effet régularisant.
Cabarrubias, Bituin C. "Existence, uniqueness and homogenization results for a class of nonlinear PDE in perforated domains." Rouen, 2012. http://www.theses.fr/2012ROUES046.
Full textAibeche, Aïssa. "Quelques problèmes non linéaires dans des domaines à frontière polygonale, comportement singulier de la solution." Nice, 1985. http://www.theses.fr/1985NICE4052.
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