Diffusion limit of a hyperbolic system with relaxation
Shi Jin, Hailiang Liu · Methods and Applications of Analysis · 1998
In this paper, we introduce a diffusive scaling to a hyperbolic system with relaxation and prove that, under such a scaling, the solution converges to that of a nonlinear convection-diffusion equation.Using energy estimates, such a limit is justified with the initial data prescribed around a traveling wave solution of the relaxation system.