Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

CT2016p

Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

​C. Christoforou, A.E. Tzavaras, Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity, to appear in Archive for Rational Mechanics and Analysis
C. Christoforou, A.E. Tzavaras
relative entropy, thermoviscoelasticity
2017
We 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 en- tropy 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.