-regularity results for quasilinear parabolic systems
Alain Bensoussan, Jens Frehse (1990)
Commentationes Mathematicae Universitatis Carolinae
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Displaying similar documents to “A counterexample in regularity theory for parabolic systems”
-regularity results for quasilinear parabolic systems
On regularity of solutions of nonlinear parabolic systems
Jindřich Nečas, Vladimír Šverák (1991)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Existence of a classical solution for linear parabolic systems of nondivergence form
Masashi Misawa (2004)
Commentationes Mathematicae Universitatis Carolinae
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We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.
Full regularity of bounded solutions to nondiagonal parabolic systems of two equations
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.