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Asymptotic behavior of degenerate logistic equations

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Arrieta Algarra, José María and Pardo San Gil, Rosa and Rodríguez Bernal, Aníbal (2015) Asymptotic behavior of degenerate logistic equations. Journal of Differential Equations, 259 (11). pp. 6368-6398. ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022039615003939


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Abstract

We analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type lambda u - n(x)u(rho). An important characteristic of this work is that the region where the logistic term n(.) vanishes, that is K-0 ={x : n(x) = 0}, may be non-smooth. We analyze conditions on lambda, rho, n(.) and K-0 guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity. The asymptotic behavior may not be the same in different parts of K-0.


Item Type:Article
Uncontrolled Keywords:Logistic nonlinearity; Asymptotic behavior; Blow up; Boundedness; Non-smooth sets; Fractal dimension
Subjects:Sciences > Mathematics > Differential equations
ID Code:35668
Deposited On:15 Feb 2016 09:57
Last Modified:12 Dec 2018 15:06

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