Convergence results for a phase transition model with vanishing microscopic acceleration

A recent phase transition model, proposed by Fremond, is based on the consideration that the microscopic movements are responsible for the phase transition at the macro- scopic level. A last version of the model, accounting also for the microscopic accelerations has been investigated in Ref. 4, where well-posedness results are established for related Cauchy{Neumann problems. The aim of this paper is the study of the asymptotic be- havior of the solution to one of the above problems, as the power of the microscopic acceleration forces goes to zero.