Reaction-Diffusion Inequalities in Cones

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Reaction-Diffusion Inequalities in Cones

Show simple item record Vaughn, Randy en Lakshmikantham, V. en 2010-06-09T14:58:56Z en 2010-06-09T14:58:56Z en 1978-02 en
dc.identifier.uri en
dc.description.abstract Recently there has been a growing interest in the study of nonlinear reaction-diffusion equations [2,3,4,7] because of the fact examples of such equations occur in population genetics [2,5,12,13], nuclear and chemical reactors [2,7,8], conduction of nerve impulses [1,7,15], and several other biological models [1,6,15]. As is the case of ordinary differential equations [9,10], it is natural to expect that the theory of reaction-diffusion inequalities and comparison theorems will play a prominent role in this study. In this paper, we consider reaction-diffusion equations which are weakly coupled relative to an arbitrary cone. We prove a result on flow-invariance which is then utilized to obtain a useful comparison theorem and a theorem on differential inequalities. The results obtained are applied to simple reaction diffusion equations to derive positivity of solutions, upper and lower bounds and stability properties. Finally we demonstrate by means of a simple example that working with a suitable cone other than [see pdf for notation] is more advantageous in the investigation of equations of reaction-diffusion. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;75 en
dc.subject Reaction-diffusion equations en
dc.subject Cones en
dc.subject Theory of reaction-diffusion inequalities en
dc.subject Comparison theorems en
dc.subject Flow-invariance en
dc.subject.lcsh Mathematics Research en
dc.title Reaction-Diffusion Inequalities in Cones en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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