Approximations of reaction-diffusion equations by interface equations : boundary-interior layer (Conference on Dynamics of Patterns in Reaction-Diffusion Systems and the Related Topics)
Kunimochi Sakamoto · Institutional Repositories DataBase (IRDB) · 2003
We deal with transition layers of the following scalar reaction-diffusion equationwith the homogeneous Neumann boundary conditions.This system, called the Allen-Cahn equation, has been studied extensively for bistable reaction kinetics.Atypical example of the nonlinearity $f$ is acubic polynomial $f(u)=u-u^{3}$ .In general, we assume that the nonlinearity $f$ is obtained from adouble-well potential $F(u)$ of equal depth.Namely, $f(u)=$ -Ff{u) with $F(u)\geq 0$ attains its absolute minimum at exactly two non-degenerate critical points $u=\pm 1$ (on-degereracy here