On the Cauchy problem for a degenerate parabolic differential equation.
El-Fiky, Ahmed (1998)
International Journal of Mathematics and Mathematical Sciences
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El-Fiky, Ahmed (1998)
International Journal of Mathematics and Mathematical Sciences
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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.
Horn, Werner (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Xiang Tao (2000)
Studia Mathematica
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For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of solvability of the Dirichlet problems.
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.
A. Grimaldi, F. Ragnedda (1983)
Annales Polonici Mathematici
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H. Ugowski (1972)
Annales Polonici Mathematici
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Łukasz Dawidowski (2017)
Open Mathematics
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In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
Philippin, G.A., Vernier Piro, S. (1999)
Journal of Inequalities and Applications [electronic only]
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D. G. Aronson, P. Besala (1967)
Colloquium Mathematicae
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J. Murzewski, A. Sowa (1972)
Applicationes Mathematicae
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P. Besala (1975)
Annales Polonici Mathematici
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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.
Arina Arkhipova (2008)
Banach Center Publications
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We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the...
P. Besala (1963)
Colloquium Mathematicae
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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.