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Chinese Annals of Mathematics, Series B

, Volume 34, Issue 2, pp 277–294 | Cite as

Increasing powers in a degenerate parabolic logistic equation

Article

Abstract

The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem
$$\partial _t u - \Delta u = au - b\left( x \right)u^p in \Omega \times \mathbb{R}^ + , u(0) = u_0 , \left. {u(t)} \right|_{\partial \Omega } = 0,$$
as p → + ∞, where Ω is a bounded domain, and b(x) is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.

Keywords

Parabolic logistic equation Obstacle problem Positive solution Increasing power Subsolution and supersolution 

2000 MR Subject Classification

35B40 35B09 35K91 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematics and CMAFUniversidade de LisboaLisboaPortugal

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