Brian H. Gilding, Roberto Natalini, and Alberto Tesei
abstract:
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.