### On integro-differential equations of parabolic type

H. Ugowski (1971)

Annales Polonici Mathematici

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H. Ugowski (1971)

Annales Polonici Mathematici

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J. Murzewski, A. Sowa (1972)

Applicationes Mathematicae

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P. Besala (1963)

Colloquium Mathematicae

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Wolf von Wahl (1983)

Annales Polonici Mathematici

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A. Wójcik (1980)

Annales Polonici Mathematici

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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...

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.

P. Besala (1975)

Annales Polonici Mathematici

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H. Ugowski (1972)

Annales Polonici Mathematici

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A. Grimaldi, F. Ragnedda (1983)

Annales Polonici Mathematici

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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].

J. Chabrowski (1974)

Colloquium Mathematicae

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Dang-Dinh Ang (1990)

Banach Center Publications

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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.

J. Chabrowski (1973)

Annales Polonici Mathematici

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