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, 2016​
C. Christoforou, A.E. Tzavaras
relative entropy, thermoviscoelasticity
2016
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hy- perbolic 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.