Semigroup Dynamics and Chaotic Behavior in Second‐Order Partial Differential Equations on H¹×L² Space

Abstract

ABSTRACT This paper focuses on the dynamics of a second‐order partial differential equation within the space described by Under suitable conditions on the parameters , and , we demonstrate that the solution of the linearized version of our proposed model generates mixing, chaotic, and distributionally chaotic strongly continuous semigroups on the product space . Additionally, our treatment of the nonhomogeneous model establishes that its solution, while not generating a strongly continuous semigroup, exhibits chaotic and distributionally chaotic behavior on the space . Moreover, we provide a compelling application of our proposed model, showcasing instances where chaos manifests.