Large Time Stability of Propagating Phase Boundaries

Abstract

We study the Cauchy problem for a 2 × 2-system of conservation laws: v t − u x = 0, u t − σ(v) t = 0 which describe the phase transition. Two constant states satisfying the Maxwell equal-area principle constitute an admissible stationary solution; a small perturbation of these Maxwell states will be our initial data. We shall show that: there exists a global in time propa gating phase boundary which is admissible in the sense that it satisfies the Abeyaratne-Knowles kinetic condition; the states outside the phase boundary tend to the Maxwell states as time goes to infinity.