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Existence of regular solutions to a class of parabolic systems in two space dimensions with critical growth behaviour

Existence of regular solutions to a class of parabolic systems in two space dimensions with... We consider parabolic systems $$u_{t} - {\rm div} \left( a(t, x, u, \nabla u)\right) + a_{0}(t, x, u, \nabla u) = 0$$ in two space dimensions with initial and Dirichlet boundary conditions. The elliptic part including a 0 is derived from a potential with quadratic growth in ∇u and is coercive and monotone. The term a 0 may grow quadratically in ∇u and satisfies a sign condition a 0 · u ≥ −K. We prove the existence of a regular long time solution verifying a regularity criterion of Arkhipova. No smallness is assumed on the data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

Existence of regular solutions to a class of parabolic systems in two space dimensions with critical growth behaviour

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-009-0071-7
Publisher site
See Article on Publisher Site

Abstract

We consider parabolic systems $$u_{t} - {\rm div} \left( a(t, x, u, \nabla u)\right) + a_{0}(t, x, u, \nabla u) = 0$$ in two space dimensions with initial and Dirichlet boundary conditions. The elliptic part including a 0 is derived from a potential with quadratic growth in ∇u and is coercive and monotone. The term a 0 may grow quadratically in ∇u and satisfies a sign condition a 0 · u ≥ −K. We prove the existence of a regular long time solution verifying a regularity criterion of Arkhipova. No smallness is assumed on the data.

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Sep 24, 2009

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