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# Analytic Semigroup Generated by the Linearization of a Riemann–Dafermos Solution

Abstract: Dafermos regularization is a viscous regularization of hyperbolic conservation laws that preserves solutions of the form u=\hat u(X/T). A Riemann–Dafermos solution is a solution of the Dafermos regularization that is close to a Riemann solution of the conservation law. Using self-similar coordinate x=X/T, Riemann–Dafermos solutions become stationary. In a suitable Banach space, we show that the linear variational system around such solution is sectorial, thus generating an analytic semigroup.

Paper:
Available from the journal web page (see below).
Author(s):
Xiao-Biao Lin,
Publishing information:
Dynamics of PDE 1, No.2, 193–207 (2004)