Asymptotic behavior of degenerate logistic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Arrieta, Jose M.^1,2  Pardo, Rosa¹  Rodriguez-Bernal, Anibal^1,2 

[1] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid, Spain

[2] UCM, UC3M, UAM, Inst Ciencias Matemat,CSIC, Madrid, Spain

关键词: Logistic nonlinearity;    Asymptotic behavior;    Blow up;    Boundedness;    Non-smooth sets;    Fractal dimension;   

DOI  :  10.1016/j.jde.2015.07.028

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free