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 “On the Hölder Continuity of Bounded Weak Solutions of Quasilinear Parabolic Systems.”
Uniqueness of positive weak solutions of second order parabolic equations
An Optimal Regularity Result For A Class Of Quasilinear Parabolic Systems.
M. Struwe, M. Giaquinta (1981)
Manuscripta mathematica
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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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Regularity for doubly nonlinear parabolic equations
Ivanov, Alexander V.
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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.
Counterexample to the regularity of weak solution of the quasilinear parabolic system
Jana Stará, Oldřich John, Jan Malý (1986)
Commentationes Mathematicae Universitatis Carolinae
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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.
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.
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.