DCDS
Hyperbolic balance laws with relaxation
Constantine M. Dafermos
Discrete & Continuous Dynamical Systems - A 2016, 36(8): 4271-4285 doi: 10.3934/dcds.2016.36.4271
This expository paper surveys the progress in a research program aiming at establishing the existence and long time behavior of $BV$ solutions to the Cauchy problem for hyperbolic systems of balance laws modeling relaxation phenomena.
keywords: heat flow. Hyperbolic balance laws relaxation viscoelasticity BV solutions
DCDS
A variational approach to the Riemann problem for hyperbolic conservation laws
Constantine M. Dafermos
Discrete & Continuous Dynamical Systems - A 2009, 23(1&2): 185-195 doi: 10.3934/dcds.2009.23.185
Within the framework of strictly hyperbolic systems of conservation laws endowed with a convex entropy, it is shown that the admissible solution to the Riemann problem is obtained by minimizing the entropy production over all wave fans with fixed end-states.
keywords: Hyperbolic conservation laws Entropy Riemann Problem

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