course: \(L^1\)-contracting semi-groups and the stability of shock profiles,II
speaker: Denis Serre (ENS-Lyon)abstract: The course deals with a non-linear variant of Markov semi-groups; they conserve the mass and satisfy a maximum principle. We focus on the example of a diffusion-convection equation \[\partial_tu+\partial_xf(u)=\partial_x^2u,\] where \(f\) is a given non-linear function.
This equation admits fronts of the form \(u(x,t)=U(x-ct)\) (\(c\) the front velocity), where \(U\) has distinct limits at \(\pm\infty\). We consider the asymptotics stability of the solution associated with an initial data \(U(x)+\phi(x)\) where \(\phi\in L^1\cap L^\infty ({\bf R})\). The stability is understood in terms of an \(L^1\)-distance, and in the sense of 'orbital stability'. This question involves tools from dynamical systems and from functional analysis.
We shall present a list other examples (unless we get short of time) where the same tools can be employed.
timetable:
Mon 24 Mar, 17:00 - 17:55, Aula Dini
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