Transition Layer Dynamics

Abstract

In a recent paper Fusco and Hale [1] attempt to explain the dynamics governing the evolution of two phases of the same substance coexisting at the transition temperature by studying the behavior of the parabolic equation

$$ {u_t} = {\varepsilon ^2}{u_{xx}} + f\left( u \right){\text{ x}} \in \Omega {\text{: = }}\left( {0,1} \right){u_x}\left( {0,t} \right) = 0 = {u_x}\left( {1,t} \right) $$

(1.1)

The variable u is the “order parameter” in the problem, which is related to the microscopic structure of the substance.