Abstract:
The relative entropy method is an efficient tool for comparing thermomechanical theories,
In this talk we will review various uses of the method in first a context of hyperbolic conservation laws
and then in contexts where a diffusion theory is approximated. Some examples of applications
will be highlighted. These include convergence of a chain of spring-mass systems to the equations
of nonlinear elasticity in the smooth regime, convergence from the equations of gas-dynamics with
friction to the porous media equation.
I will also present a framework for convergence from gas dynamics with
friction to gradient flows describing diffusion theories.
The latter will be applied to the convergence from Euler-Poisson with attracting potential
to Keller-Segel type systems. Also, for convergence from the
Korteweg theory with friction to Cahn-Hilliard type equations. |