Stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in N-dimensional domains |
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Authors: | Arnaldo Simal do Nascimento |
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Institution: | Universidade Federal de S. Carlos DM, 13565-905, S. Carlos, S.P., Brazil |
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Abstract: | We prove existence and establish the asymptotic behavior, as ε→0, of stable stationary solutions to the equation ut=ε∇·d(x)∇u]+(1−u2)u−a(x)], for , where , N?2, with Neumann boundary condition. The function a(x)∈C0,ν(Ω) satisfies −1<a(x)<1 and vanishes on some hypersurfaces. The results generalize to N-dimensional domains and to variable diffusivity earlier paper by Angenent et al. (J. Differential Equations 67 (1987) 212). |
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