Thursday, 26 November 2015, 3 p.m. (sharp), Stefano Melchionna, University of Vienna, at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
WED APPROACH TO DISSIPATIVE PROBLEMS AND APPLICATIONS
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
Given a target dissipative problem (P), the so-called Weighted Energy-Dissipation (WED) procedure consists in defining a global parameter dependent functional I_epsilon over trajectories and proving that its minimizers converge up to subsequences to solutions to the target system (P) as the parameter epsilon goes to 0. Such a global-in-time variational approach to evolution problems is interesting, since it paves the way to the application of tools and techniques of the calculus of variation (e.g. Direct Method, relaxation, Gamma-convergence) in the evolutive setting. This brings also a new tool for checking qualitative properties of solutions and comparison principles. Moreover, the minimization problem features, typically, more regular solutions, since the Euler-Lagrange system
associated with the minimization of I_epsilon corresponds to an elliptic-in-time regularisation (P)^epsilon of the original problem (P). By combining the minimization of a WED type functional and a fixed point argument, we prove existence of solutions to an elliptic-in-time regularization of nonpotential perturbations of gradient flows and convergence for epsilon that goes to 0. We also apply the WED formalism to check qualitative properties of solutions
and comparison principles for some classes of dissipative equations.
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