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|Title: ||Asymmetric spotty patterns for the Gray-Scott model in R^2|
|Authors: ||Winter, M|
|Keywords: ||Asymmetric patterns; Spotty solutions|
Self-replication; Reaction-diffusion system
|Publication Date: ||2003|
|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:||Mathematical Science|
Dept of Mathematics Research Papers
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