C. M. Cuesta, S. Hittmeir and C. Schmeiser

Kinetic shock profiles for nonlinear hyperbolic conservation laws

Pages 139-198
Received: 30 January 2009
Accepted: 16 March 2009
Mathematics Subject Classification (2000): 35L67 - 82D05

Keywords: Kinetic equations, shock profiles, hyperbolic conservation laws.

Abstract: A unified framework for studying the existence and stability of kinetic shock profiles is presented. This includes small amplitude waves for the situation when the macroscopic model is a hyperbolic system of conservation laws with genuine nonlinearity. For the case of scalar conservation laws, also large amplitude waves can be understood. Applications range from BGK-models for general scalar conservation laws and for gas dynamics, to an equation for fermions in a scattering background under the action of an electric field and to the Boltzmann equation of gas dynamics.