On
variational formulation of entropy
solutions to nonlinear conservation laws
Eitan
Tadmor
and
Abstract:
A
proper notion of weak solutions for nonlinear conservation laws
requires such
solutions to be entropic. Entropy solutions are found to
be at the
crossroads, when reached from a microscopic description of
kinetic formulation
or from a macroscopic description as vanishing viscosity limits.
In both cases,
entropy solutions were also interpreted within a proper
variational framework.
The
notion
of entropy, which is intimately connected with symmetry, is an
extension
imposed on nonlinear systems conservation laws. In this
context, K. O.
Friedrichs in his 1979 John von Neumann Lecture, asked
“Now,
in
many branches of physics … symmetries play a fundamental role,
but all these
symmetries—as it seems to me—are assumed and not derived. I
now wonder whether
or not … symmetries can also be derived.”
In
this
lecture I will give a concise overview on the theory and
computation of entropy
solutions for nonlinear conservation laws, and I will present a
new variational
formulation which addresses the question raised by Friedrichs.