Global existence of solutions of parabolic problems with nonlinear boundary conditions
Pavol Quittner (1996)
Banach Center Publications
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Pavol Quittner (1996)
Banach Center Publications
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Gary Lieberman (1996)
Banach Center Publications
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Wojciech Zajączkowski (1996)
Banach Center Publications
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Existence of weak solutions and an -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.
Poppenberg, Markus (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Kordoš, M. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Pudełko, Anna (2004)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Jan Cholewa, Tomasz Dlotko (2000)
Banach Center Publications
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An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
Arina A. Arkhipova (2001)
Commentationes Mathematicae Universitatis Carolinae
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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.
Quittner, Pavol (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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M. Kirane (1993)
Applicationes Mathematicae
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This paper considers a reaction-diffusion system with biatic diffusion.Existence of a globally bounded solution is proved and its large timebehaviour is given.