A RELATIVE ENTROPY APPROACH TO CONVERGENCE OF A LOW ORDER APPROXIMATION TO A NONLINEAR ELASTICITY MODEL WITH VISCOSITY AND CAPILLARITY

摘要

In this paper we study the dynamics of an elastic bar undergoing phase transitions. It is modeled by two regularizations of the equations of nonlinear elastodynamics with a nonconvex energy. We estimate the difference between solutions to the two regularizations if in one of them a coupling parameter is sent to infinity. This estimate is based on an adaptation of the relative entropy framework using the regularizing terms in order to compensate for the nonconvexity of the energy density.