FRONT INTERACTION AND NONHOMOGENEOUS EQUILIBRIA FOR TRISTABLE REACTION-DIFFUSION EQUATIONS

The authors investigate the interfacial dynamics associated with three -phase systems and the possible occurrence of steady multiphase patter ns in one and higher space dimensions. The model for this study is a G inzburg-Landau model for phase transitions given by the partial differ ential equation u(t) = epsilonDELTAu - 1/epsilon V(u)epsilon(u). defin ed for x in a domain OMEGA subset-of R(n) and t > 0. The potential V(e psilon) is assumed to possess three wells having depths within O(epsil on) of each other. The evolution of the solution can be described by t racking the motion of fronts connecting adjacent wells of V(epsilon). The primary interest is to understand how the self-induced motion of a given front is affected by the presence of a second nearby front. Thi s interaction is characterized precisely using the formal method of ma tched asymptotic expansions. In some settings, this leads to the predi ction of steady waves linking the outer two phases across a thin regio n of the intermediate phase. A rigorous proof of the existence of stab le equilibria having this profile is given using the techniques of Gam ma-convergence.