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Extremal equilibria for reaction–diffusion equations in bounded domains and applications
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Rodríguez-Bernal, Aníbal and Vidal-López, Alejandro (2008) Extremal equilibria for reaction–diffusion equations in bounded domains and applications. Journal of Differential Equations, Vol.244 (No.12). pp. 2983-3030. doi:10.1016/j.jde.2008.02.046 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2008.02.046
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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Differential Equations | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-0396 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.244 | ||||
Number: | No.12 | ||||
Page Range: | pp. 2983-3030 | ||||
DOI: | 10.1016/j.jde.2008.02.046 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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