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Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 30 lipca 2024

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1

Yung, Tamara. "Traffic Modelling Using Parabolic Differential Equations." Thesis, Linköpings universitet, Kommunikations- och transportsystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-102745.

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The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow;

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2

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the s

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3

Baysal, Arzu. "Inverse Problems For Parabolic Equations." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.

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In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in Problem I and II). If solution of inverse proble

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4

Keras, Sigitas. "Numerical methods for parabolic partial differential equations." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/251611.

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5

Ascencio, Pedro. "Adaptive observer design for parabolic partial differential equations." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/49454.

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This thesis addresses the observer design problem, for a class of linear one-dimensional parabolic Partial Differential Equations, considering the simultaneous estimation of states and parameters from boundary measurements. The design is based on the Backstepping methodology for Partial Differential Equations and extends its central idea, the Volterra transformation, to compensate for the parameters uncertainties. The design steps seek to reject time-varying parameter uncertainties setting forth a type of differential boundary value problems (Kernel-PDE/ODEs) to accomplish its objective, the s

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6

Williams, J. F. "Scaling and singularities in higher-order nonlinear differential equations." Thesis, University of Bath, 2003. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275878.

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7

Tsang, Siu Chung. "Preconditioners for linear parabolic optimal control problems." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.

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In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and A

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8

Rivera, Noriega Jorge. "Some remarks on certain parabolic differential operators over non-cylindrical domains /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025649.

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9

Hammer, Patricia W. "Parameter identification in parabolic partial differential equations using quasilinearization." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/37226.

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We develop a technique for identifying unknown coefficients in parabolic partial differential equations. The identification scheme is based on quasilinearization and is applied to both linear and nonlinear equations where the unknown coefficients may be spatially varying. Our investigation includes derivation, convergence, and numerical testing of the quasilinearization based identification scheme<br>Ph. D.

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10

Prinja, Gaurav Kant. "Adaptive solvers for elliptic and parabolic partial differential equations." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/adaptive-solvers-for-elliptic-and-parabolic-partial-differential-equations(f0894eb2-9e06-41ff-82fd-a7bde36c816c).html.

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In this thesis our primary interest is in developing adaptive solution methods for parabolic and elliptic partial differential equations. The convection-diffusion equation is used as a representative test problem. Investigations are made into adaptive temporal solvers implementing only a few changes to existing software. This includes a comparison of commercial code against some more academic releases. A novel way to select step sizes for an adaptive BDF2 code is introduced. A chapter is included introducing some functional analysis that is required to understand aspects of the finite element

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11

Marlow, Robert. "Moving mesh methods for solving parabolic partial differential equations." Thesis, University of Leeds, 2010. http://etheses.whiterose.ac.uk/1528/.

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In this thesis, we introduce and assess a new adaptive method for solving non-linear parabolic partial differential equations with fixed or moving boundaries, using a moving mesh with continuous finite elements. The evolution of the mesh within the interior of the spatial domain is based upon conserving the distribution of a chosen monitor function across the domain throughout time, where the initial distribution is based upon the given initial data. For the moving boundary cases, the mesh movement at the boundary is governed by a second monitor function. The method is applied with different m

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12

Mavinga, Nsoki. "Nonlinear second order parabolic and elliptic equations with nonlinear boundary conditions." Birmingham, Ala. : University of Alabama at Birmingham, 2008. https://www.mhsl.uab.edu/dt/2009r/mavinga.pdf.

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Thesis (Ph. D.)--University of Alabama at Birmingham, 2008.<br>Title from PDF title page (viewed Sept. 23, 2009). Additional advisors: Inmaculada Aban, Alexander Frenkel, Wenzhang Huang, Yanni Zeng. Includes bibliographical references.

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13

Sahimi, Mohd S. "Numerical methods for solving hyperbolic and parabolic partial differential equations." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/12077.

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The main object of this thesis is a study of the numerical 'solution of hyperbolic and parabolic partial differential equations. The introductory chapter deals with a general description and classification of partial differential equations. Some useful mathematical preliminaries and properties of matrices are outlined. Chapters Two and Three are concerned with a general survey of current numerical methods to solve these equations. By employing finite differences, the differential system is replaced by a large matrix system. Important concepts such as convergence, consistency, stability and acc

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14

Taj, Malik Shahadat Ali. "Higher order parallel splitting methods for parabolic partial differential equations." Thesis, Brunel University, 1995. http://bura.brunel.ac.uk/handle/2438/5780.

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The thesis develops two families of numerical methods, based upon new rational approximations to the matrix exponential function, for solving second-order parabolic partial differential equations. These methods are L-stable, third- and fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods second-order spatial derivatives are approximated by new difference approximations. Then parallel algorithms are developed and tested on one-, two- and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions

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15

Blake, Kenneth William. "Moving mesh methods for non-linear parabolic partial differential equations." Thesis, University of Reading, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369545.

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16

Teichman, Jeremy Alan 1975. "Bounding of linear output functionals of parabolic partial differential equations." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50440.

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17

Zhang, Lan. "Parameter identification in linear and nonlinear parabolic partial differential equations." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/37762.

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18

Leahy, James-Michael. "On parabolic stochastic integro-differential equations : existence, regularity and numerics." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10569.

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In this thesis, we study the existence, uniqueness, and regularity of systems of degenerate linear stochastic integro-differential equations (SIDEs) of parabolic type with adapted coefficients in the whole space. We also investigate explicit and implicit finite difference schemes for SIDEs with non-degenerate diffusion. The class of equations we consider arise in non-linear filtering of semimartingales with jumps. In Chapter 2, we derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by Lévy driven stochastic differential equations (SDEs) with adap

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19

Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

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20

Agueh, Martial Marie-Paul. "Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29180.

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21

Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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22

Jürgens, Markus. "A semigroup approach to the numerical solution of parabolic differential equations." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=976761580.

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23

Ngounda, Edgard. "Numerical Laplace transformation methods for integrating linear parabolic partial differential equations." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2735.

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Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2009.<br>ENGLISH ABSTRACT: In recent years the Laplace inversion method has emerged as a viable alternative method for the numerical solution of PDEs. Effective methods for the numerical inversion are based on the approximation of the Bromwich integral. In this thesis, a numerical study is undertaken to compare the efficiency of the Laplace inversion method with more conventional time integrator methods. Particularly, we consider the method-of-lines based on MATLAB’s ODE15s and the Crank-Nicolson method. Our studies include

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24

Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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25

Jakubowski, Volker G. "Nonlinear elliptic parabolic integro differential equations with L-data existence, uniqueness, asymptotic /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=966250141.

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26

Smyshlyaev, Andrey S. "Explicit and parameter-adaptive boundary control laws for parabolic partial differential equations." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3235014.

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Thesis (Ph. D.)--University of California, San Diego, 2006.<br>Title from first page of PDF file (viewed December 6, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 181-186).

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27

Utz, Tilman [Verfasser]. "Control of Parabolic Partial Differential Equations Based on Semi-Discretizations / Tilman Utz." Aachen : Shaker, 2012. http://d-nb.info/1069046574/34.

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28

Stanciulescu, Vasile Nicolae. "Selected topics in Dirichlet problems for linear parabolic stochastic partial differential equations." Thesis, University of Leicester, 2010. http://hdl.handle.net/2381/8271.

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This thesis is devoted to the study of Dirichlet problems for some linear parabolic SPDEs. Our aim in it is twofold. First, we consider SPDEs with deterministic coefficients which are smooth up to some order of regularity. We establish some theoretical results in terms of existence, uniqueness and regularity of the classical solution to the considered problem. Then, we provide the probabilistic representations (the averaging-over-characteristic formulas of its solution. We, thereafter, construct numerical methods for it. The methods are based on the averaging-over-characteristic formula and th

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29

Grepl, Martin A. (Martin Alexander) 1974. "Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32387.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.<br>Includes bibliographical references (p. 243-251).<br>Modern engineering problems often require accurate, reliable, and efficient evaluation of quantities of interest, evaluation of which demands the solution of a partial differential equation. We present in this thesis a technique for the prediction of outputs of interest of parabolic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced-basis approximations - Galerkin projection onto a space WN spanned by s

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30

Kadhum, Nashat Ibrahim. "The spline approach to the numerical solution of parabolic partial differential equations." Thesis, Loughborough University, 1988. https://dspace.lboro.ac.uk/2134/6725.

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This thesis is concerned with the Numerical Solution of Partial Differential Equations. Initially some definitions and mathematical background are given, accompanied by the basic theories of solving linear systems and other related topics. Also, an introduction to splines, particularly cubic splines and their identities are presented. The methods used to solve parabolic partial differential equations are surveyed and classified into explicit or implicit (direct and iterative) methods. We concentrate on the Alternating Direction Implicit (ADI), the Group Explicit (GE) and the Crank-Nicolson (C-

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31

Düll, Wolf-Patrick. "Theorie einer pseudoparabolischen partiellen Differentialgleichung zur Modelliurung der Lösemittelaufnahme in Polymerfeststoffen." Bonn : Mathematisches Institut der Universität, 2004. http://catalog.hathitrust.org/api/volumes/oclc/62771307.html.

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32

Chen, Mingxiang. "Structural stability of periodic systems." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29341.

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33

Kuhn, Zuzana. "Ranges of vector measures and valuations." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/30875.

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34

Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is rev

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35

BACCOLI, ANTONELLO. "Boundary control and observation of coupled parabolic PDEs." Doctoral thesis, Università degli Studi di Cagliari, 2016. http://hdl.handle.net/11584/266880.

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Reaction-diffusion equations are parabolic Partial Differential Equations (PDEs) which often occur in practice, e.g., to model the concentration of one or more substances, distributed in space, under the in uence of different phenomena such as local chemical reactions, in which the substances are transformed into each other, and diffusion, which causes the substances to spread out over a surface in space. Certainly, reaction-diffusion PDEs are not confined to chemical applications but they also describe dynamical processes of non-chemical nature, with examples being found in thermodynam

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36

Hall, Eric Joseph. "Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8038.

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First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference a

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37

Johnsen, Pernilla. "Homogenization of Partial Differential Equations using Multiscale Convergence Methods." Licentiate thesis, Mittuniversitetet, Institutionen för matematik och ämnesdidaktik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-42036.

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The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of th

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38

Zhang, Chun Yang. "A second order ADI method for 2D parabolic equations with mixed derivative." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592940.

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39

Portal, Pierre. "Harmonic analysis of banach space valued functions in the study of parabolic evolution equations /." free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p3137737.

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40

Wang, Xince. "Quasilinear PDEs and forward-backward stochastic differential equations." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/17383.

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In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs.

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41

Fetter, Nathansky Alfredo. "Fehlerabschätzungen für Finite-Elemente Approximationen von parabolischen Variationsungleichungen." Bonn : [s.n.], 1986. http://catalog.hathitrust.org/api/volumes/oclc/17488340.html.

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42

Wilderotter, Olga. "Adaptive finite elemente Methode für singuläre parabolische Probleme." Bonn : [s.n.], 2001. http://catalog.hathitrust.org/api/volumes/oclc/48077903.html.

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43

Flaig, Thomas G. [Verfasser]. "Discretization strategies for optimal control problems with parabolic partial differential equations / Thomas G. Flaig." München : Verlag Dr. Hut, 2013. http://d-nb.info/103729176X/34.

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44

Tang, Shaowu [Verfasser]. "Multiscale and geometric methods for linear elliptic and parabolic partial differential equations / Shaowu Tang." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2008. http://d-nb.info/1034787411/34.

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45

Vieira, Nelson Felipe Loureiro. "Theory of the parabolic Dirac operators and its applications to non-linear differential equations." Doctoral thesis, Universidade de Aveiro, 2009. http://hdl.handle.net/10773/2924.

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46

Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

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47

Bal, Kaushik. "Some Contribution to the study of Quasilinear Singular Parabolic and Elliptic Equations." Thesis, Pau, 2011. http://www.theses.fr/2011PAUU3032/document.

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Les travaux réalisés dans cette thèse concernent l’étude de problèmes quasi-linéaires paraboliques et elliptiques singuliers. Par singularité, nous signifions que le problème fait intervenir une non linéarité qui explose au bord du domaine où l’équation est posée. La présence du terme singulier entraine un manque de régularité des solutions. Ce défaut de régularité génère en conséquence un manque de compacité qui ne permet pas d’appliquer directement les méthodes classiques d’analyse non linéaires pour démontrer l’existence de solutions et discuter les propriétés de régularité et de comporteme

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48

Meyer, John Christopher. "Theoretical aspects of the Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4222/.

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The aim of this thesis is to provide a generic approach to the study of semi-linear parabolic partial differential equations when the nonlinearity fails to be Lipschitz continuous, but is in the class of Hӧlder continuous functions or the class of upper Lipschitz continuous functions. New results are obtained concerning the well-posedness (in the sense of Hadamard) of the initial value problem, namely, uniqueness and conditional continuous dependence results for upper Lipschitz continuous nonlinearities, and an existence result for Hӧlder continuous nonlinearities. To obtain these results, two

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49

Cao, Yanzhao. "Analysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equations." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/37771.

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The exact controllability problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of appropriate optimal controls. A numerical scheme of computing exact controls for linear parabolic equations is constructed based on this result. To obtain numerical approximation of the exact control for the Burger's equation, we first construct another numerical scheme of computing exa

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50

Moreno, Claudia. "Control of partial differential equations systems of dispersive type." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASV031.

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Il existe peu de résultats dans la littérature sur la contrôlabilité du système d'équations aux dérivées partielles. Dans cette thèse, nous considérons l'étude des propriétés de contrôle pour trois systèmes couplés d'équations aux dérivées partielles de type dispersif et un problème inverse de récupération d’un coefficient. Le premier système est formé par N équations de Korteweg-de Vries sur un réseau en forme d'étoile. Pour ce système, nous étudierons la contrôlabilité exacte avec N contrôles placés aux extrémités du réseau. Le deuxième système couple trois équations de Korteweg-de Vries. Ce

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