Stable viscosity matrices for systems of conservation laws |
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Authors: | Andrew Majda Robert L Pego |
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Affiliation: | Department of Mathematics, University of California, Berkeley, California 94720 USA;Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 USA |
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Abstract: | A natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension, u1 + f(u)x = 0, u?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. |
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