ABSTRACT
This chapter concerns singular limits of stiff relaxation and dominant diffusion for general 2 × 2 nonlinear systems of conservation laws, that is, the relaxation time tends to zero faster than the diffusion parameter. It presents theorems and proof for the stiff relaxation and dominant diffusion. The chapter gives some important physical models such as the system of elasticity, the isentropic system of gas dynamics in Eulerian coordinates, and the extended models of traffic flows with relaxation terms. It also concerns the zero relaxation and dissipation limits for some physical models, without bounded L∞ estimates, such as the system of isentropic gas dynamics in Lagrangian coordinates.
