Singular limits of stiff relaxation and dominant diffusion for nonlinear systems (Q1598393)

The author considers a \(2 \times 2\) system of conservation laws with relaxation and diffusion: \[ v_t + f(v,u)_x = \varepsilon v_{xx} , \] \[ u_t + g(v,u)_x + \tfrac{1}{\tau}\alpha(v,u) (u - h(v)) = \varepsilon u_{xx}. \] The following general principle is established: If there exists a uniform a priori bound independent of \(\varepsilon\), then any solution sequence converges for \(\varepsilon \to 0\), \(\tau = o(\varepsilon)\) to the corresponding equilibrium solution of this system. Several applications are given including the system of nonlinear elasticity and isentropic gas dynamics.