Mathematics – Analysis of PDEs
Scientific paper
2007-09-26
Journal of Differential Equations 245 (2008) 505-565
Mathematics
Analysis of PDEs
Scientific paper
We consider an Allen-Cahn type equation with a bistable nonlinearity associated to a double-well potential whose well-depths can be slightly unbalanced, and where the coefficient of the nonlinear reaction term is very small. Given rather general initial data, we perform a rigorous analysis of both the generation and the motion of interface. More precisely we show that the solution develops a steep transition layer within a small time, and we present an optimal estimate for its width. We then consider a class of reaction-diffusion systems which includes the FitzHugh-Nagumo system as a special case. Given rather general initial data, we show that the first component of the solution vector develops a steep transition layer and that all the results mentioned above remain true for this component.
Alfaro Matthieu
Hilhorst Danielle
Matano Hiroshi
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