Increasing Powers in a Degenerate Parabolic Logistic Equation



The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem
$$\partial_t u-\Delta u=a u-b(x) u^p \quad\text{in } \varOmega\times \mathbb{R} ^+,\quad u(0)=u_0,\quad u(t)|_{\partial \varOmega}=0, $$
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.


Parabolic logistic equation Obstacle problem Positive solution Increasing power, subsolution and supersolution 

Mathematics Subject Classification

35B40 35B09 35K91 



The second author would like to thank Jesús Hernández and Pedro Freitas for the useful discussions related with this paper.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics and CMAFUniversidade de LisboaLisboaPortugal

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