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• W2080428609 abstract "We consider the equation $e^{2}Delta u=(u-a(x))(u^2-1)$ in $Omega$, $frac{partial u}{partial nu} =0$ on $partial Omega$, where $Omega$ is a smooth and bounded domain in $R^n$, $nu$ the outer unit normal to $paOmega$, and $a$ a smooth function satisfying $-1<a(x)<1$ in $ov{Omega}$. We set $K$, $Omega_+$ and $Omega_-$ to be respectively the zero-level set of $a$, {a>0} and {a<0}. Assuming $nabla a neq 0$ on $K$ and $ane 0$ on $partial Omega$, we show that there exists a sequence $e_j to 0$ such that the above equation has a solution $u_{e_j}$ which converges uniformly to $pm 1$ on the compact sets of $O_{pm}$ as $j to + infty$." @default.
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• W2080428609 date "2008-06-01" @default.
• W2080428609 modified "2023-10-17" @default.
• W2080428609 title "Transition layer for the heterogeneous Allen–Cahn equation" @default.
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• W2080428609 doi "https://doi.org/10.1016/j.anihpc.2007.03.008" @default.
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