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Extremal equilibria for reaction-diffusion equations in bounded domains and applications

Authors :
Alejandro Vidal-López
Aníbal Rodríguez-Bernal
Source :
E-Prints Complutense: Archivo Institucional de la UCM, Universidad Complutense de Madrid, E-Prints Complutense. Archivo Institucional de la UCM, instname
Publication Year :
2008
Publisher :
Elsevier, 2008.

Abstract

We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equation.

Details

Language :
English
Database :
OpenAIRE
Journal :
E-Prints Complutense: Archivo Institucional de la UCM, Universidad Complutense de Madrid, E-Prints Complutense. Archivo Institucional de la UCM, instname
Accession number :
edsair.doi.dedup.....cecbb1d0be0cfd5e12238f1cc8026d81