Changchun Liu (2013)
Annales Polonici Mathematici
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We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.
Vladimír Ďurikovič (1979)
Annales Polonici Mathematici
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Kaouther Ammar, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
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We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
Pao-Liu Chow (2015)
Banach Center Publications
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The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem. ...
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.
P. Besala (1983)
Annales Polonici Mathematici
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V. Lj. Kocić (1985)
Matematički Vesnik
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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.
Andrzej Borzymowski, Jacek Urbanowicz (1983)
Annales Polonici Mathematici
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Zhou, Jun (2007)
Surveys in Mathematics and its Applications
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Horn, Werner (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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H. Ugowski (1972)
Annales Polonici Mathematici
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Ivanov, Alexander V.
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Mikhail Borsuk (2002)
Annales Polonici Mathematici
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We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.