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.