Chaotic semigroups for a higher order partial differential equation in Herzog-type space of analytic functions

Abstract

We present comprehensive criteria for specific parameters to ensure both Devaney chaos and distributional chaos within the context of the $C_0$-semigroup solutions associated with the Moore–Gibson–Thompson equation, which belongs to a class of higher order partial differential equations. We demonstrate that this $C_0$-semigroup exhibits a strongly mixing measure with full support in cases of chaos. Furthermore, we provide a critical parameter that enables us to distinguish between stability and chaos within these semigroups in the Herzog-type space of analytic functions.