Variational methods for young measure solutions of nonlinear parabolic evolutions of forward-backward type and of high spatial order

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Non-Convex potentials are associated to the formation of oscillations and fine microstructure; dynamics are governed by nonlinear evolutions of forward-backward type which typically admit no classical solutions. In the case of a model dynamical problem it is shown that a Young measure solution exists, is unique and converges time-asymptotically to a unique limit point which is a solution of the equilibrium equation. The potential gradient and the identity function are independent variables with respect to the Young measure.