Pattern Formations for a Strong Interacting Free Boundary Problem

In this paper we consider the system of reaction-diffusion-advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. In strong competition case, we study the influence of competition rates on the long time behavior of solutions and prove t...

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Veröffentlicht in:	Acta applicandae mathematicae 2017-04, Vol.148 (1), p.121-142
Hauptverfasser:	Zhou, Ling, Zhang, Shan, Liu, Zuhan
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Applied mathematics Calculus of Variations and Optimal Control Optimization Competition Computational Mathematics and Numerical Analysis Ecology Formations Free boundaries Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Partial Differential Equations Population growth Probability Theory and Stochastic Processes Studies Theorems
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Zusammenfassung:	In this paper we consider the system of reaction-diffusion-advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. In strong competition case, we study the influence of competition rates on the long time behavior of solutions and prove that two species spatially segregate as the competition rates become large. Besides, by using a blow up method, we obtain the uniform Hölder bounds for solutions of the system.
ISSN:	0167-8019 1572-9036
DOI:	10.1007/s10440-016-0081-2