Sengul, Yasemin (2010) Wellposedness of dynamics of microstructure in solids. PhD thesis, University of Oxford.

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Abstract
In this thesis, the problem of wellposedness of nonlinear viscoelasticity under the assumptions allowing for phase transformations in solids is considered. In one space dimension we prove existence and uniqueness of the solutions for the quasistatic version of the model using approximating sequences corresponding to the case when initial data takes finitely many values. This special case also provides upper and lower bounds for the solutions which are interesting in their own rights. We also show equivalence of the existence theory we develop with that of gradient flows when the storedenergy function is assumed to be convex. Asymptotic behaviour of the solutions as time goes to infinity is then investigated and stabilization results are obtained by means of a new argument. Finally, we look at the problem from the viewpoint of curves of maximal slope and follow a timediscretization approach. We introduce a threedimensional method based on composition of timeincrements, as a result of which we are able to deal with the physical requirement of frameindifference. In order to test this method and distinguish the difficulties for possible generalizations, we look at the problem in a convex setting. At the end we are able to obtain convergence of the minimization scheme as time step goes to zero.
Item Type:  Thesis (PhD) 

Subjects:  H  N > Mechanics of deformable solids O  Z > Partial differential equations D  G > Dynamical systems and ergodic theory 
Research Groups:  Oxford Centre for Nonlinear PDE 
ID Code:  1748 
Deposited By:  Eprints Administrator 
Deposited On:  20 Aug 2013 08:28 
Last Modified:  29 May 2015 19:26 
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