ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
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 isO(t −3/4+1/2p+σ) inL p , 1≦p≦∞, with σ〉0 being arbitrarily small.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02099669
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