Relative entropy in hyperbolic relaxation for balance laws

Relative Entropy in Hyperbolic Relaxation for Balance Laws

We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative entropy. We provide a direct proof of convergence in the smooth regime for a wide class of physical systems. We present results for systems arising in materials sc...

Relative Entropy in Hyperbolic Relaxation

We provide a framework so that hyperbolic relaxation systems are endowed with a relative entropy identity. This allows a direct proof of convergence in the regime that the limiting solution is smooth.

Hyperbolic Conservation Laws with Stii Relaxation Terms and Entropy

We study the limiting behavior of systems of hyperbolic conservation laws with stii relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N N systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown t...

Relative Entropy in Diffusive Relaxation

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoela...

An Entropy Condition and Global Existence Result for Hyperbolic Balance Laws