Dynamics of Partial Differential Equations

Volume 1 (2004)

Number 2

Analytic semigroup generated by the linearization of a Riemann-Dafermos solution

Pages: 193 – 207

DOI: http://dx.doi.org/10.4310/DPDE.2004.v1.n2.a2

Author

Xiao-Biao Lin (Department of Mathematics, North Carolina State University, Raleigh, N.C., U.S.A.)

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.

Keywords

Dafermos regularization, hyperbolic conservation law, Riemann-Dafermos solution, analytic semigroup

2010 Mathematics Subject Classification

Primary 35-xx. Secondary 46-xx.

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