Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws
Resource
Communications in Mathematical Physics,138,51-61.
Journal
Communications in Mathematical Physics
Journal Volume
138
Journal Issue
1
Pages
51-61
Date Issued
1991
Author(s)
Abstract
We study the large-time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system. The initial data considered here is a perturbation of a constant state. It is shown that the solutions converge to single-mode diffusion waves in directions of strictly hyperbolic fields, and to multiple-mode diffusion waves in directions of nonstrictly hyperbolic fields. The multiple-mode diffusion waves, which are the new elements here, are the self-similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields, with the nonlinear fluxes replaced by their quadratic parts. The convergence rate to these diffusion waves is O(t-3/4+1/2 p+σ) in Lp, 1≦p≦∞, with σ>0 being arbitrarily small. © 1991 Springer-Verlag.
SDGs
Type
journal article