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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. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use J 7 = 1 Jdoi:10.2307/1999914 fatcat:vbyhb5btsbejnopxmf4yytv7xi