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 Long-time behavior for semilinear degenerate parabolic equations on $\mathbb{R}^N$ Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 751-766 https://doi.org/10.4134/CKMS.2013.28.4.751Printed October 1, 2013 Cung The Anh and Le Thi Thuy Hanoi National University of Education, Electric Power University Abstract : We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\R^N$: $$\frac{\partial u}{\partial t} - \text{div}(\sigma (x)\nabla u) + \lambda u+ f(u) = g(x),$$ under a new condition concerning a variable non-negative diffusivity $\sigma(\cdot)$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method. Keywords : semilinear degenerate parabolic equation, weak solution, global attractor, non-compact case, tail estimates method Downloads: Full-text PDF

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