Abstract: Microstructures in phhase-transitions of alloys can be modeled by the energy minimization of a non-convex energy density . Their time-evolution leads to a nonlinear wave equation with the non-monotone stress functions and proper bo undary and initial conditions. This hyperbolis initial-boundary value problem is expected to allow, in general, solely Young measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding very weak sense. It can be shown that discrete soluutions exist and generate weakly convergent subsequences whose limit is a Young measure solution. Numerical examples in one space dimension illustrate the time-evolving microstructure of a nonlinearly vibrating string.

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