| Abstract: |
| In this talk, we consider the 1-dimensional Schnackenberg model on the interval (-1,1) with heterogeneity g(x) in front of the nonlinearity under the Neumann boundary condition. Here, g(x) is a given positive, symmetric, i.e. g(x)=g(-x), and Lipschitz continuous function. For a certain singular perturbation regime, first we construct a symmetric 1-peak stationary solution by using the contraction mapping theorem with precise asymptotic behaviors. Next, for more smooth g(x), we study the stability of the constructed statinary solution.
Especially, we reveal the effect of the heterogeneity g(x) on the stability.
(This is a joint work with Dr. Yuta Ishii). |
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