Concerning solutions of an exterior boundary-value problem for a system of non-linear parabolic equations
P. Besala (1964)
Annales Polonici Mathematici
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P. Besala (1964)
Annales Polonici Mathematici
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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.
Vladimír Ďurikovič (1979)
Annales Polonici Mathematici
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H. Ugowski (1973)
Annales Polonici Mathematici
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Cung The Anh, Phan Quoc Hung (2008)
Annales Polonici Mathematici
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We study the global existence and long-time behavior of solutions for a class of semilinear degenerate parabolic equations in an arbitrary domain.
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 (1963)
Colloquium Mathematicae
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Ji Liu, Jia-Shan Zheng (2015)
Czechoslovak Mathematical Journal
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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of...
P. Besala (1975)
Annales Polonici Mathematici
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Philippin, G.A., Vernier Piro, S. (1999)
Journal of Inequalities and Applications [electronic only]
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Wolf von Wahl (1983)
Annales Polonici Mathematici
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Herbert Amann (1991)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Piotr Biler, Tadeusz Nadzieja (2011)
Colloquium Mathematicae
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This note presents an elementary approach to the nonexistence of solutions of linear parabolic initial-boundary value problems considered in the Feller test.
Horn, Werner (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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