Remarks on the stability of shock profiles for conservation laws with dissipation

Pego, Robert L.

doi:10.1090/S0002-9947-1985-0797065-0

Remarks on the stability of shock profiles for conservation laws with dissipation
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Trans. Amer. Math. Soc. 291 (1985), 353-361 Request permission

Abstract:

Two remarks are made. The first is to establish the stability of monotone shock profiles of the KdV-Burgers equation, based on an energy method of Goodman. The second remark illustrates, specifically in Burgers’ equation, that uniform rates of decay are not to be expected for perturbations of shock profiles in typical norms.

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