Chaotic semigroups from second order partial differential equations

Abstract

[EN] We give general conditions on given parameters to ensure Devaney and distributional chaos for the solution C-0-semigroup corresponding to a class of second-order partial differential equations. We also provide a critical parameter that led us to distinguish between stability and chaos for these semigroups. In the case of chaos, we prove that the Co-semigroup admits a strongly mixing measure with full support. We also give concrete examples of partial differential equations, such as the telegraph equation, whose solutions satisfy these properties. (C) 2017 Elsevier Inc. All rights reserved.