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Description: |
This talk will be on the problem of well-posedness of nonlinear viscoelasticity under the assumptions allowing for phase transformations in solids. In one space dimension existence and uniqueness of the solutions for the quasistatic version of the model is proved by means of approximating sequences corresponding to the case when the initial data takes finitely many values. Also, equivalence of the existence theory developed with that of gradient flows is showed when the stored-energy function is assumed to be $\lambda$-convex. Asymptotic behaviour of solutions as time goes to infinity is also investigated and stabilization results are obtained. Finally, the problem is considered from the viewpoint of curves of maximal slope and a time-discretization approach is followed. A new method based on composition of time-increments is introduced as a result of which one can deal with the physical requirement of frame-indifference.
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