Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed -norm.
Weidemaier, Peter (2002)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Weidemaier, Peter (2002)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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J. Chabrowski (1973)
Annales Polonici Mathematici
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P. Besala (1964)
Annales Polonici Mathematici
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H. Ugowski (1973)
Annales Polonici Mathematici
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Gerd Grubb (1995)
Mathematische Zeitschrift
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W. M. Zajączkowski
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The existence and uniqueness of solutions of an initial-boundary value problem for the second order linear parabolic system which appears in free boundary problems for compressible Navier-Stokes equations are proved. Moreover, an estimate in anisotropic Sobolev-Slobodetskii spaces with noninteger derivatives is found. The existence and regularity of solutions are shown by means of a regularizer in the same way as in the case of general parabolic systems. However, the problem must be...
Giovanni Dore, Alberto Venni (1991)
Mathematische Zeitschrift
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Vladimír Ďurikovič (1979)
Annales Polonici Mathematici
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J. Kačur (1983)
Banach Center Publications
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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...
Sufang Tang, Pengcheng Niu (2010)
Rendiconti del Seminario Matematico della Università di Padova
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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.
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.
Ahmed Aberqi, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
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We prove the existence of a renormalized solution to a class of doubly nonlinear parabolic systems.
Oleh Buhrii, Nataliya Buhrii (2017)
Open Mathematics
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Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.
Wolf von Wahl (1983)
Annales Polonici Mathematici
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J. Murzewski, A. Sowa (1972)
Applicationes Mathematicae
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