# Analysis Seminar @CMUC November 26 2010

Analysis Seminar @CMUC (Center for Mathematics of the University of Coimbra)

 URL: https://cmuc.mat.uc.pt/rdonweb/event/showPPSeminar.do?seminarID=1055

Well-posedness of dynamics of microstructure in solids
Yasemin Sengul (CMUC)

Abstract: 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.

Date: November, 26 (Friday), 14h30.

Room 5.5

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