Extremal equilibria for monotone semigroups in ordered spaces with application to evolutionary equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Cholewa, Jan W.²  Rodriguez-Bernal, Anibal^1,3 

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

[2] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

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

关键词: Monotone semigroups;    Equilibria;    Asymptotic behavior of solutions;    Dissipativeness;    Attractors;    Parabolic equations and systems;    Degenerate problems;    Damped wave equations;   

DOI  :  10.1016/j.jde.2010.04.006

来源: Elsevier

【 摘 要 】

We consider monotone semigroups in ordered spaces and give general results concerning the existence of extremal equilibria and global attractors. We then show some applications of the abstract scheme to various evolutionary problems, from ODEs and retarded functional differential equations to parabolic and hyperbolic PDEs. In particular, we exhibit the dynamical properties of semigroups defined by semilinear parabolic equations in RN with nonlinearities depending on the gradient of the solution. We consider as well systems of reaction-diffusion equations in RN and provide some results concerning extremal equilibria of the semigroups corresponding to damped wave problems in bounded domains or in RN. We further discuss some nonlocal and quasilinear problems, as well as the fourth order Cahn-Hilliard equation. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free