Uniqueness of positive weak solutions of second order parabolic equations
D. G. Aronson (1965)
Annales Polonici Mathematici
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Displaying similar documents to “Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents”
Uniqueness of positive weak solutions of second order parabolic equations
A nonlinear degenerate parabolic equation
B. H. Gilding (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
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.
On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.
Michael Struwe, Mariano Giaquinta (1982)
Mathematische Zeitschrift
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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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Regularity for doubly nonlinear parabolic equations
Ivanov, Alexander V.
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On behaviour of non-negative weak solutions of parabolic equations at the boundary
J. Chabrowski (1972)
Colloquium Mathematicae
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On internal approximations of parabolic problems
H. Marcinkowska (1983)
Annales Polonici Mathematici
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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.
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.
Full regularity of bounded solutions to nondiagonal parabolic systems of two equations
Dmitry Portnyagin (2008)
Applicationes Mathematicae
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Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.