Abstract
A natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension, u1 + f(u)x = 0, uε{lunate}Rm, is studied. These matrices are admissible in the sense that small-amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system ut + f(u)x = v(Dux)x as ifv → 0 if D is in this class. The class is determined by a linearized stability requirement: The Cauchy problem for the equation u1 + f′(u0) ux = vDuxx should be well posed in L2 uniformly in v as v → 0. Previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion.
Original language | English (US) |
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Pages (from-to) | 229-262 |
Number of pages | 34 |
Journal | Journal of Differential Equations |
Volume | 56 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1985 |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics