Displaying similar documents to “Global L ∞ bounds for a class of quasilinear parabolic equations.”

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis

Piotr Biler, Lorenzo Brandolese (2009)

Studia Mathematica

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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.

Parabolic sublinear operators with rough kernel generated by parabolic calderön-zygmund operators and parabolic local campanato space estimates for their commutators on the parabolic generalized local morrey spaces

Ferit Gurbuz (2016)

Open Mathematics

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In this paper, the author introduces parabolic generalized local Morrey spaces and gets the boundedness of a large class of parabolic rough operators on them. The author also establishes the parabolic local Campanato space estimates for their commutators on parabolic generalized local Morrey spaces. As its special cases, the corresponding results of parabolic sublinear operators with rough kernel and their commutators can be deduced, respectively. At last, parabolic Marcinkiewicz operator...

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.

Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

Yutaro Chiyo (2023)

Archivum Mathematicum

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This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.

The parabolic-parabolic Keller-Segel equation

Kleber Carrapatoso (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

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I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].