Dynamics of Partial Differential Equations
Volume 1 (2004)
Analytic semigroup generated by the linearization of a Riemann-Dafermos solution
Pages: 193 – 207
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.
Dafermos regularization, hyperbolic conservation law, Riemann-Dafermos solution, analytic semigroup
2010 Mathematics Subject Classification
Primary 35-xx. Secondary 46-xx.