Chaotic -semigroups induced by semiflows in Lebesgue and Sobolev spaces

We give characterizations of chaos for C 0 -semigroups induced by semiflows on L ρ p ( Ω ) for open Ω ⊆ R similar to the characterizations of hypercyclicity and mixing of such C 0 -semigroups proved in [18]. Moreover, we characterize hypercyclicity, mixing, and chaos for these classes of C 0 -semigroups on W ⁎ 1 , p ( I ) for a bounded interval I ⊂ R and prove that these C 0 -semigroups are never hypercyclic on W 1 , p ( I ) . We apply our results to concrete first order partial differential equations, such as the von Foerster–Lasota equation.