SEMINAR @ SISSSA, prof. Denis Serre - course

[Barbara Corzani]

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FUNCTIONAL ANALYSIS SECTOR'S ACTIVITIES
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On January 8-11, SlSSA, professor Denis Serre, UMPA Ecole Normale Superieure de Lyon, will give a course on:

Dissipative mechanisms in systems of conservation laws

Various dissipative mechanisms: viscosity, relaxation, coupling with elliptic equations, BGK models, ... Dissipative limit vs time asymptotics.

Dissipation and entropy. A priori estimate. 

Linear theory: Well-posedness for the Cauchy problem, time asymptotics, relaxation limit. Kawashima's condition ; link with control theory. Various instances of the sub-characteristic property.

Discontinuities. How shocks are approached in dissipative structures: shock profiles. Can discontinuities happen in dissipative structures ?

Nonlinear setting. Entropy formalism. Characteristic fields in hyperbolic-parabolic or hyperbolic-elliptic systems. Nonlinear diffusion waves, asymptotic decay. The scalar case; L^1 stability of travelling waves.

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Denis Serre does not need any introduction: he is one of the most famous 
mathematicians working in hyperbolic systems.
His papers have influenced deeply all topics in non linear systems, and his 
books have been a fundamental reference for researchers in this field. He has 
won several prices for his most famous papers.

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