A simple characterization of chaos for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces

Abstract

We give a simple characterization of chaos for weighted composition $C_0$-semigroups on $L_{\rho }^p(\Omega )$ for an open interval $\Omega \subseteq \mathbb{R}$. Moreover, we characterize chaos for these classes of $C_0$-semigroups on the closed subspace $W_{\ast }^{1,p}(\Omega )$ of the Sobolev space $W^{1,p}(\Omega )$ for a bounded interval $\Omega \subset \mathbb{R}$. These characterizations simplify previously obtained characterization of chaos for these classes of $C_0$-semigroups.

arXiv comment11 pages