Increasing Powers in a Degenerate Parabolic Logistic Equation |
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Authors: | José Francisco RODRIGUES Hugo TAVARES |
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Institution: | Department of Mathematics and CMAF, Universidade de Lisboa, Avenida Professor Gama Pinto 2,1649-003 Lisboa, Portugal |
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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. |
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Keywords: | Parabolic logistic equation Obstacle problem Positive solution Increasing power Subsolution and supersolution |
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