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Energy, dissipation, and evolutionary Gamma convergence for gradient systems | Prof. Alexander Mielke (Weierstrass Institute Berlin und Humboldt University Berlin)

Kurzbeschreibung:
Startdatum: 18.12.2018 - 16:00
Enddatum: 18.12.2018 - 17:30
Adresse: MZH 6210
Organisator/Ansprechpartner:,
Preis: 0€

Many ordinary and partial differntial equations can be written as
a gradient flow, which means that there is an energy functional
that drives the evolution of the the solutions by flowing down
in the energy landscape. The gradient is given in terms of a
dissipation structure, which in the simplest case is a Riemannian
metric. We discuss classical and nontrivial new examples in
chemical reactions and in quantum master equations.

Considering a family of gradient systems depending on a small
parameter, it is natural to ask for the limiting (also called
effective) gradient system if the parameter tends to 0. This can be
achieved based on De Giorgi's Energy-Dissipation Principle (EDP). We
discuss several versions of EDP convergence and show by examples that
the theory is flexible enough to allow for situations where starting
from quadratic dissipation potentials we arrive at physically
relevant, effective dissipation potentials that are no longer
quadratic.

Einladung von Prof. Jens Rademacher