On the existence of the weak solution of a boundary value problem arising in the theory of water percolation
J. Goncerzewicz (1980)
Applicationes Mathematicae
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Displaying similar documents to “On behaviour of non-negative weak solutions of parabolic equations at the boundary”
On the existence of the weak solution of a boundary value problem arising in the theory of water percolation
Weak Solutions for a Fourth Order Degenerate Parabolic Equation
Changchun Liu, Jinyong Guo (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.
Concerning solutions of an exterior boundary-value problem for a system of non-linear parabolic equations
P. Besala (1964)
Annales Polonici Mathematici
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On a certain non-linear initial-boundary value problem for integro-differential equations of parabolic type
H. Ugowski (1973)
Annales Polonici Mathematici
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Uniqueness of positive weak solutions of second order parabolic equations
D. G. Aronson (1965)
Annales Polonici Mathematici
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On the Hölder Continuity of Bounded Weak Solutions of Quasilinear Parabolic Systems.
Michael Struwe (1981)
Manuscripta mathematica
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Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents
Lingeshwaran Shangerganesh, Arumugam Gurusamy, Krishnan Balachandran (2017)
Communications in Mathematics
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In this work, we study the existence and uniqueness of weak solutions of fourth-order degenerate parabolic equation with variable exponent using the difference and variation methods.
Non-linear stationary parabolic boundary value problems in an infinite cylinder
Vladimír Ďurikovič (1979)
Annales Polonici Mathematici
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On internal approximations of parabolic problems
H. Marcinkowska (1983)
Annales Polonici Mathematici
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Regularity for doubly nonlinear parabolic equations
Ivanov, Alexander V.
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A generalization of the maximum principle to nonlinear parabolic systems
Dmitry Portnyagin (2003)
Annales Polonici Mathematici
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A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.
Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems
Sachiko Ishida, Tomomi Yokota (2023)
Archivum Mathematicum
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This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.
Extension of a result of Ladyženskaja and Uralceva concerning second-order parabolic equations of arbitrary order
Wolf von Wahl (1983)
Annales Polonici Mathematici
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Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
Tuomo Kuusi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.