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Long-time behavior for semilinear degenerate parabolic equations on RN

Le Thi Thuy|Cung The Anh
대한수학회 (The Korean Mathematical Society)|2013.10|대한수학회논문집 (Communications of the KMS)|제28권 제4호|pp. 751-766

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참고문헌

키워드

weak solutionglobal attractorsemilinear degenerate parabolic equationnon-compact casetail estimates method
주제분류수학

초록

We study the existence and long-time behavior of solutionsto the following semilinear degenerate parabolic equation on RN:∂u∂t− div(σ(x)∇u) + λu + f(u) = g(x), under a new condition concerning a variable non-negative diffusivity σ(·). Some essential difficulty caused by the lack of compactness of Sobolevembeddings is overcome here by exploiting the tail-estimates method.

Abstract

We study the existence and long-time behavior of solutionsto the following semilinear degenerate parabolic equation on RN:∂u∂t− div(σ(x)∇u) + λu + f(u) = g(x), under a new condition concerning a variable non-negative diffusivity σ(·). Some essential difficulty caused by the lack of compactness of Sobolevembeddings is overcome here by exploiting the tail-estimates method.

참고문헌 (18)

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