The attractor for a nonlinear reaction‐diffusion system in an unbounded domain
MA Efendiev, SV Zelik - … on Pure and Applied Mathematics: A …, 2001 - Wiley Online Library
Communications on Pure and Applied Mathematics: A Journal Issued …, 2001•Wiley Online Library
In this paper the quasi‐linear second‐order parabolic systems of reaction‐diffusion type in
an unbounded domain are considered. Our aim is to study the long‐time behavior of
parabolic systems for which the nonlinearity depends explicitly on the gradient of the
unknown functions. To this end we give a systematic study of given parabolic systems and
their attractors in weighted Sobolev spaces. Dependence of the Hausdorff dimension of
attractors on the weight of the Sobolev spaces is considered.© 2001 John Wiley & Sons, Inc.
an unbounded domain are considered. Our aim is to study the long‐time behavior of
parabolic systems for which the nonlinearity depends explicitly on the gradient of the
unknown functions. To this end we give a systematic study of given parabolic systems and
their attractors in weighted Sobolev spaces. Dependence of the Hausdorff dimension of
attractors on the weight of the Sobolev spaces is considered.© 2001 John Wiley & Sons, Inc.
Abstract
In this paper the quasi‐linear second‐order parabolic systems of reaction‐diffusion type in an unbounded domain are considered. Our aim is to study the long‐time behavior of parabolic systems for which the nonlinearity depends explicitly on the gradient of the unknown functions. To this end we give a systematic study of given parabolic systems and their attractors in weighted Sobolev spaces. Dependence of the Hausdorff dimension of attractors on the weight of the Sobolev spaces is considered. © 2001 John Wiley & Sons, Inc.
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