Displaying similar documents to “A generalization of the maximum principle to nonlinear parabolic systems”

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.

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.

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 note on the paper of Y. Naito

Piotr Biler (2006)

Banach Center Publications

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This note contains some remarks on the paper of Y. Naito concerning the parabolic system of chemotaxis and published in this volume.