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|Title:||Asymmetric spotty patterns for the Gray-Scott model in R^2|
|Keywords:||Asymmetric patterns; Spotty solutions;Self-replication; Reaction-diffusion system|
|Citation:||Stud Appl Math 110(2003): 63-102|
|Abstract:||In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k_1,\,k_2, there are asymmetric solutions with k_1 large spots (type A) and k_2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetric solutions are shown to be unstable. However, in a narrow range of parameters, asymmetric solutions may be stable.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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