Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity
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AbstractWe extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.
SponsorsResearch partially supported by the European Commission ITN project ”Modeling and computation of shocks and interfaces”. AET acknowledges the support of the King Abdullah University of Science and Technology (KAUST).