Chaotic C0-semigroups induced by semiflows in Lebesgue and Sobolev spaces

We give characterizations of chaos for C0-semigroups induced by semiflows on Lρp(Ω) for open Ω⊆R similar to the characterizations of hypercyclicity and mixing of such C0-semigroups proved in [18]. Moreover, we characterize hypercyclicity, mixing, and chaos for these classes of C0-semigroups on W⁎1,p(I) for a bounded interval I⊂R and prove that these C0-semigroups are never hypercyclic on W1,p(I). We apply our results to concrete first order partial differential equations, such as the von Foerster-Lasota equation.