Existence, Nonexistence and uniqueness of solutions for classes of reaction-diffusion systems arising in ecosystems with nonlinear boundary conditions
Subject Areas : Analyze
Abdoljavad Shabanpour
1
,
S.H. Rasouli
2
*
1 - Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Babol, Iran
2 - Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Babol, Iran
Keywords: Positive solutions, Sub-super solutions, Reaction-diffusion, Population dynamic, Alee effect,
Abstract :
Recently, there has been a growing interest in the study of reaction-diffusion models. In this article, we investigate the existence, non-existence and uniqueness of solutions for a class of reaction-diffusion systems with nonlinear boundary conditions. Such systems are proposed in population biology (of two species) and the results obtained can be used in population management. The understanding of mechanisms and pattern of spatial dispersal of interacting species is a central problem in biology and ecology, and biochemical reactions. Boundary conditions indicate the tension between members when they arrive in the region, leave the region, or remain in the region. To prove theorems, we use the method of sub-super solutions. In the beginning, we will deal with the preliminaries in this regard. In the second part, we will introduce three topics with a lemma, which we are going to prove in this article, and in the third part, we will prove the theorems.
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