Brian H. Gilding, Roberto Natalini, and Alberto Tesei

How Parabolic Free Boundaries Approximate Hyperbolic Fronts

Some recent results concerning existence and qualitative behaviour of the boundaries of the suppurts of solutions of the Cauchy problem for nonlinear first--order hyperbolic and second-order parabolic scalar conservation laws are discussed. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.

Mathematics Subject Classification: 35L65, 35K55, 35K65, 35L67, 35R35.

Key words and phrases: Conservation laws, convection--diffusion equations, shock waves, enthropy solutions, speed of propagation, vanishing viscosity limit.