Introduction into entropy and duality methods for reaction-diffusion systems
Thời gian: 09:00 đến 15:30 Ngày 30/06/2016
Địa điểm: C2-714
Báo cáo viên: Klemens Fellner
Tóm tắt:The so-called entropy method for evaluating the large-time-behaviour of dissipative systems goes back
to original ideas of Boltzmann and Grad and consists in quantifying the dissipation of a convex entropy functional
in terms of the relative entropy towards entropy minimising equilibrium states.
In proving functional inequalities which hold independently from the flow of the PDE model,
the entropy method avoids linearisation and is able to prove global convergence towards an equilibrium with constants and rates, which can be estimated explicitly.
In this course, we shall present an introduction to entropy methods for reaction-diffusion type models and
apply the obtained functional inequalities to prove explicit exponential convergence towards equilibrium for a large class of reaction-diffusion systems.
Moreover, we shall address results and open problems in obtaining global solutions (renormalised, weak or classical)
to nonlinear reaction-diffusion systems, where the absence of comparison principles leads to significant difficulties in ensuring the integrability of the nonlinear terms