Relevant bibliographies by topics / Degenerate equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Degenerate equation'

Author: Grafiati
Published: 9 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Degenerate equation"

1

Trudinger, Neil S. "On degenerate fully nonlinear elliptic equations in balls." Bulletin of the Australian Mathematical Society 35, no. 2 (1987): 299–307. http://dx.doi.org/10.1017/s0004972700013253.

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We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.
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PERTHAME, BENOÎT, and ALEXANDRE POULAIN. "Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility." European Journal of Applied Mathematics 32, no. 1 (2020): 89–112. http://dx.doi.org/10.1017/s0956792520000054.

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The degenerate Cahn–Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual Cahn–Hilliard equation with a singular single-well potential and degenerate mobility. These degeneracy and singularity induce numerous difficulties, in particular for its numerical simulation. To overcome these issues, we propose a relaxation system formed of two second-order equations which can be solved with standard packages. This system is endowed with an ener
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Agosti, A. "Error analysis of a finite element approximation of a degenerate Cahn-Hilliard equation." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (2018): 827–67. http://dx.doi.org/10.1051/m2an/2018018.

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This work considers a Cahn-Hilliard type equation with degenerate mobility and single-well potential of Lennard-Jones type, motivated by increasing interest in diffuse interface modelling of solid tumors. The degeneracy set of the mobility and the singularity set of the potential do not coincide, and the zero of the potential is an unstable equilibrium configuration. This feature introduces a nontrivial difference with respect to the Cahn-Hilliard equation analyzed in the literature. In particular, the singularities of the potential do not compensate the degeneracy of the mobility by constrain
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Oza, Priyank. "Fully nonlinear degenerate equations with applications to Grad equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 26 (2024): 1–13. http://dx.doi.org/10.14232/ejqtde.2024.1.26.

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We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations: { | D u | γ M λ , Λ + ( D 2 u ( x ) ) = f ( | u ≥ u ( x ) | ) in Ω u = g on ∂ Ω , where γ ≥ 1 is a constant, Ω is a bounded domain in R N with C 1 , 1 boundary. We prove the existence of a W 2 , p -viscosity solution to the above equation, which degenerates when the gradient of the solution vanishes.
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Igisinov, S. Zh, L. D. Zhumaliyeva, A. O. Suleimbekova, and Ye N. Bayandiyev. "Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (2022): 51–58. http://dx.doi.org/10.31489/2022m3/51-58.

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In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure
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Mai, La-Su, and Suriguga. "Local well-posedness of 1D degenerate drift diffusion equation." Mathematics in Engineering 6, no. 1 (2024): 155–72. http://dx.doi.org/10.3934/mine.2024007.

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<abstract><p>This paper proves the well-posedness of locally smooth solutions to the free boundary value problem for the 1D degenerate drift diffusion equation. At the free boundary, the drift diffusion equation becomes a degenerate hyperbolic-Poisson coupled equation. We apply the Hardy's inequality and weighted Sobolev spaces to construct the appropriate a priori estimates, overcome the degeneracy of the system and successfully establish the existence of solutions in the Lagrangian coordinates.</p></abstract>
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Nazarova, K. "ON ONE METHOD FOR OBTAINING UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR AN INTEGRO-DIFFERENTIAL EQUATION." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy), no. 1 (March 15, 2022): 42–54. http://dx.doi.org/10.47526/2022-2/2524-0080.04.

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The modified method of parametrization is used to study a linear Fredholm integro-differential equation with a degenerate kernel. Using the fundamental matrix, the conditions are established for the existence of a solution to the special Cauchy problem for the Fredholm integro-differential equation with a degenerate kernel. A system of linear algebraic equations is constructed with respect to the introduced additional parameters. Conditions for the unique solvability of a linear boundary value problem for the Fredholm integro-differential equation with a degenerate kernel are obtained.
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Pasichnyk, H. "SOLUTIONS OF SOME INTEGRAL EQUATIONS OF THE SECOND KIND." Bukovinian Mathematical Journal 12, no. 1 (2024): 84–93. http://dx.doi.org/10.31861/bmj2024.01.08.

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The article examines the solutions of some integral equations of the second kind. Such equations arise when using Levi's method to construct a fundamental solution of the Cauchy problem for a degenerate equation of the Kolmogorov type. The equation may also contain a degeneracy on the initial hyperplane. The coefficients of this equation are bounded in the group of principal terms and ones are increasing functions in the group of lowest terms. The considered classes of kernels of integral equations make it possible to preserve the function that determines the growth of the coefficients of the
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Christodoulou, Dimitris M., Eric Kehoe, and Qutaibeh D. Katatbeh. "Degenerate Canonical Forms of Ordinary Second-Order Linear Homogeneous Differential Equations." Axioms 10, no. 2 (2021): 94. http://dx.doi.org/10.3390/axioms10020094.

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For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations a
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Shakhmurov, V. B., and Н. К. Musaev. "Nonlocal separable elliptic and parabolic equations and applications." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 1 (February 5, 2025): 66–92. https://doi.org/10.26907/0021-3446-2025-1-66-92.

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The regularity properties of nonlocal anisotropic elliptic equations with parameters are investigated in abstract weighted Lp spaces. The equations include the variable coefficients and abstract operator function A = A (x) in a Banach space E in leading part. We find the sufficient growth assumptions on A and appropriate symbol polynomial functions that guarantee the uniformly separability of the linear problem. It is proved that the corresponding anisotropic elliptic operator is sectorial and is also the negative generator of an analytic semigroup. Byusing these results, the existence and uni
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Dissertations / Theses on the topic "Degenerate equation"

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Tepoyan, L. "The mixed problem for a degenerate operator equation." Universität Potsdam, 2008. http://opus.kobv.de/ubp/volltexte/2009/3033/.

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We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.
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Brinkschulte, Judith. "The Cauchy-Riemann equation with support conditions in domains with Levi degenerate boundaries." [S.l.] : [s.n.], 2002. http://dochost.rz.hu-berlin.de/dissertationen/brinkschulte-judith-2002-04-19.

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Picard, Sebastien. "A priori estimates of the degenerate Monge-Ampère equation on compact Kähler manifolds." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119756.

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The regularity theory of the degenerate complex Monge-Ampère equation is studied. First, the equation is considered on a compact Kahler manifold without boundary. Accordingly, some background information on Kahler geometry is presented. Given a solution of the degenerate complex Monge-Ampère equation, it is shown that its oscillation and gradient can be bounded. The Laplacian of the solution is also estimated. There is a slight improvement from the literature on the conditions required in order to obtain the estimate on the Laplacian of the solution, however the estimates developed only hold i
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Brinkschulte, Judith. "The Cauchy-Riemann equation with support conditions on domains with Levi-degenerate boundaries." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14734.

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In einem ersten Teil betrachten wir ein relativ kompaktes Gebiet Omega einer n-dimensionalen Kähler-Mannigfaltigkeit, mit Lipschitz-Rand, welches eine gewisse "log delta"-Pseudokonvexität besitzt. Wir zeigen, dass die Cauchy-Riemann Gleichung mit exaktem Träger in Omega für alle Bigrade (p,q) mit 0< q< n-1 eine Lösung besitzt. Ausserdem ist das Bild des Cauchy-Riemann Operators auf glatten (p,n-1)-Formen mit exaktem Träger in Omega abgeschlossen. Wir geben Anwendungen für die Lösbarkeit der tangentialen Cauchy-Riemann Gleichungen für glatte Formen und Ströme auf Rändern von schwach pseudokonve
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Mattioli, Mauro. "Estimates on degenerate jump-diffusion processes and regularity of the related valuation equation." Doctoral thesis, Luiss Guido Carli, 2011. http://hdl.handle.net/11385/200886.

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Many risk-neutral pricing problems proposed in the finance literature require to be dealt with by solving the corresponding Partial Integro-Differential Equation. Unfortunately, neither the standard Sobolev spaces theory, or the present literature on viscosity solution theory is able to deal with some problems of interest in finance. A recent result presented by Costantini, Papi and D’Ippoliti accepted for pubblication on Finance and Stochastics [17], shows that, under general conditions on the coefficients of the stochastic integro-differential equation, whenever a Lyapunov-type condition is
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Watling, K. D. "Formulae for solutions to (possibly degenerate) diffusion equations exhibiting semi-classical and small time asymptotics." Thesis, University of Warwick, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380277.

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ROCCHETTI, DARIO. "Generation of analytic semigroups for a class of degenerate elliptic operators." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/749.

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Questa tesi è suddivisa in due capitoli. Nel primo si da un risultato di buona positura per una classe di problemi parabolici degeneri. I risultati ottenuti, validi in dimensione 2, garantiscono che le soluzioni di tali problemi supportano l'integrazione per parti. Nel secondo capitolo, si studia la controllabilità allo zero per una classe di operatori parabolici degeneri in forma non-divergenza. In particolare, i coefficienti del termine del secondo ordine possono degenerare al bordo del dominio spaziale. A questo scopo si giunge previo una disuguaglianza di osservabilità per il pro
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Rao, Arvind Satya. "Weak solutions to a Monge-Ampère type equation on Kähler surfaces." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/582.

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In the context of moment maps and diffeomorphisms of Kähler manifolds, Donaldson introduced a fully nonlinear Monge-Ampère type equation. Among the conjectures he made about this equation is that the existence of solutions is equivalent to a positivity condition on the initial data. Weinkove later affirmed Donaldson's conjecture using a gradient flow for the equation in the space of Kähler potentials of the initial data. The topic of this thesis is the case when the initial data is merely semipositive and the domain is a closed Kähler surface. Regularity techniques for degenerate Monge-Ampère
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URBANI, CRISTINA. "Bilinear Control of Evolution Equations." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/10061.

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The thesis is devoted to the study of the stabilization and the controllability of the evolution equations $$u'(t) + Au (t) + p (t) Bu (t) = 0$$ by means of a bilinear control $p$. Bilinear controls are coefficients of the equation that multiply the state variable. Multiplicative controls are therefore suitable to describe processes that change their principal parameters in presence of a control. We first present a result of rapid stabilization of the parabolic equations towards the ground state by bilinear control with a doubly exponential rate of convergence. Under stronger hypothese
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Boiger, Wolfgang Josef. "Stabilised finite element approximation for degenerate convex minimisation problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16790.

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Infimalfolgen nichtkonvexer Variationsprobleme haben aufgrund feiner Oszillationen häufig keinen starken Grenzwert in Sobolevräumen. Diese Oszillationen haben eine physikalische Bedeutung; Finite-Element-Approximationen können sie jedoch im Allgemeinen nicht auflösen. Relaxationsmethoden ersetzen die nichtkonvexe Energie durch ihre (semi)konvexe Hülle. Das entstehende makroskopische Modell ist degeneriert: es ist nicht strikt konvex und hat eventuell mehrere Minimalstellen. Die fehlende Kontrolle der primalen Variablen führt zu Schwierigkeiten bei der a priori und a posteriori Fehlerschätz
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Books on the topic "Degenerate equation"

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Wakako, Hideaki. Exact WKB analysis for the degenerate third Painleve equation of type (Ds). Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2007.

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Levendorskii, Serge. Degenerate Elliptic Equations. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6.

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DiBenedetto, Emmanuele. Degenerate Parabolic Equations. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0895-2.

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Levendorskiĭ, Serge. Degenerate elliptic equations. Kluwer, 1993.

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DiBenedetto, Emmanuele. Degenerate parabolic equations. Springer-Verlag, 1993.

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Favini, Angelo, and Gabriela Marinoschi. Degenerate Nonlinear Diffusion Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28285-0.

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Favini, Angelo. Degenerate Nonlinear Diffusion Equations. Springer Berlin Heidelberg, 2012.

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A, Dzhuraev. Degenerate and other problems. Longman Scientific and Technical, 1992.

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Ahmed, Zeriahi, ed. Degenerate complex Monge--Ampère equations. European Mathematical Society Publishing House, 2017.

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Favini, A. Degenerate differential equations in Banach spaces. Marcel Dekker, 1999.

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Book chapters on the topic "Degenerate equation"

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Arrieta, José M., Rosa Pardo, and Aníbal Rodríguez-Bernal. "A Degenerate Parabolic Logistic Equation." In Advances in Differential Equations and Applications. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_1.

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Galaktionov, Victor A., and Sergey A. Posashkov. "On Some Monotonicity in Time Properties for a Quasilinear Parabolic Equation with Source." In Degenerate Diffusions. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0885-3_5.

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Wu, Lizhou, and Jianting Zhou. "Improved Linear and Nonlinear Iterative Methods for Rainfall Infiltration Simulation." In Rainfall Infiltration in Unsaturated Soil Slope Failure. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-9737-2_4.

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AbstractThe linear infiltration equations obtained by discretizing Richards’ equation need to be solved iteratively, including two approaches of linear and nonlinear iterations. The first method is to use numerical methods to directly numerically discretize Richards’ equations to obtain nonlinear ordinary differential equations and then use nonlinear iterative methods to iteratively solve, such as Newton’s method (Radu et al. in On the convergence of the Newton method for the mixed finite element discretization of a class of degenerate parabolic equation. Numerical mathematics and advanced app
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Efendiev, Messoud. "Porous medium equation in homogeneous media: Long-time dynamics." In Attractors for Degenerate Parabolic Type Equations. American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/04.

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Efendiev, Messoud. "Porous medium equation in heterogeneous media: Long-time dynamics." In Attractors for Degenerate Parabolic Type Equations. American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/05.

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Rodrigues, José Francisco, and Hugo Tavares. "Increasing Powers in a Degenerate Parabolic Logistic Equation." In Partial Differential Equations: Theory, Control and Approximation. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-41401-5_15.

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Krejčí, Pavel. "Boundedness of Solutions to a Degenerate Diffusion Equation." In Springer INdAM Series. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64489-9_12.

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Slathia, Geetika, Rajneet Kaur, Kuldeep Singh, and Nareshpal Singh Saini. "Forced KdV Equation in Degenerate Relativistic Quantum Plasma." In Nonlinear Dynamics and Applications. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99792-2_2.

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Fragnelli, Genni, and Dimitri Mugnai. "The Case of an Interior Degenerate/Singular Parabolic Equation." In SpringerBriefs in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69349-7_5.

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Fragnelli, Genni, and Dimitri Mugnai. "The Case of a Boundary Degenerate/Singular Parabolic Equation." In SpringerBriefs in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69349-7_4.

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Conference papers on the topic "Degenerate equation"

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Sanchez, A. D., S. Chaitanya Kumar, and M. Ebrahim-Zadeh. "Mean-field equation for phase-modulation mode-locked optical parametric oscillator with dispersion control." In CLEO: Applications and Technology. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_at.2024.jw2a.180.

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We derive a mean-field equation for degenerate optical parametric oscillator driven by a continuous-wave laser with intracavity electro-optic modulator, including dis-persion compensation. The equation predicts femtosecond-pulse formation in both normal and anomalous dispersion regimes.
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Xu, Ming, and Renjun Qiu. "Minimal-norm solution for Fredholm integral equation of the first kind with degenerate kernel implemented in finite steps." In 2024 14th International Conference on Information Technology in Medicine and Education (ITME). IEEE, 2024. https://doi.org/10.1109/itme63426.2024.00133.

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Allan, Douglas A., Anca Ostace, Andrew Lee, et al. "Jacobian-based Model Diagnostics and Application to Equation Oriented Modeling of a Carbon Capture System." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.160262.

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Equation-oriented (EO) modeling has the potential to enable the effective design and optimization of the operation of advanced energy systems. However, advanced modeling of energy systems results in a large number of variables and non-linear equations, and it can be difficult to search through these to identify the culprit(s) responsible for convergence issues. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms so t
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Song, Zeyuan, and Zheyu Jiang. "A Physics-based, Data-driven Numerical Framework for Anomalous Diffusion of Water in Soil." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.163304.

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Precision modeling and forecasting of soil moisture are essential for implementing smart irrigation systems and mitigating agricultural drought. Most agro-hydrological models are based on the standard Richards equation, a highly nonlinear, degenerate elliptic-parabolic partial differential equation (PDE) with first order time derivative. However, research has shown that standard Richards equation is unable to model preferential flow in soil with fractal structure. In such a scenario, the soil exhibits anomalous non-Boltzmann scaling behavior. Incorporating the anomalous non-Boltzmann scaling b
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a, Zeyu, and Zheyu Ji a. "A Novel Bayesian Framework for Inverse Problems in Precision Agriculture." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.113662.

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An essential problem in precision agriculture is to accurately model and predict root-zone (top 1 m of soil) soil moisture profile given soil properties and precipitation and evapotranspiration information. This is typically achieved by solving agro-hydrological models. Nowadays, most of these models are based on the standard Richards equation (RE), a highly nonlinear, degenerate elliptic-parabolic partial differential equation that describes irrigation, precipitation, evapotranspiration, runoff, and drainage through soils. Recently, the standard RE has been generalized to time-fractional RE w
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Goncerzewicz, Jan. "On the initial-boundary value problems for a degenerate parabolic equation." In Parabolic and Navier–Stokes equations. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-13.

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BRESCH, DIDIER, and PIERRE-EMMANUEL JABIN. "QUANTITATIVE ESTIMATES FOR ADVECTIVE EQUATION WITH DEGENERATE ANELASTIC CONSTRAINT." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0134.

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Butuzov, Valentin Fedorovich. "Singularly perturbed ODEs with multiple roots of the degenerate equation." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc22964.

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"Solvability of the quasilinear degenerate equation with Dzhrbashyan — Nersesyan derivative." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.84.

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Шуклина, Анна, and Марина Плеханова. "Mixed control of solutions to a degenerate nonlinear fractional equation." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh2t-2021-10-06.47.

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Reports on the topic "Degenerate equation"

1

Fujisaki, Masatoshi. Normed Bellman Equation with Degenerate Diffusion Coefficients and Its Application to Differential Equations. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada190319.

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Nohel, John A. A Class of One-Dimensional Degenerate Parabolic Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada160962.

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Gupta, V., B. H. J. McKellar, and D. D. Wu. The degeneracy of the free Dirac equation. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/6105369.

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