Optimal interface width for the Allen-Cahn equation (Dynamics of spatio - temporal patterns for the system of reaction - diffusion equations)
Matthieu Alfaro, Danielle Hilhorst, Hiroshi Matano · Institutional Repositories DataBase (IRDB) · 2005
We revisit the parabolic problem for the Allen-Cahn equationwhere $\epsilon$ is asmall parameter and $f$ abistable nonlinearity More precisely wc assume that $f$ is smooth and has exactly three zeros $\alpha_{-}0$ , (1.1) and that $\int_{\alpha-}^{\alpha_{+}}f(u)du$ $=0$ .(1.2)