Chaotic semigroups from second order partial differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Alberto Conejero, J.¹  Lizama, Carlos²  Murillo-Arcila, Marina³ 

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, E-46022 Valencia, Spain

[2] Univ Santiago Chile, Dept Matemat & Ciencia Computac, Estn Cent, Las Sophoras 173, Santiago, Chile

[3] Univ Jaume 1, Dept Matemat, Campus Riu Sec, E-12071 Castellon de La Plana, Spain

关键词: Devaney chaos;    Hypercyclicity;    C-0-semigroups;    Dynamics of C-0-semigroups;    Telegraph equation;   

DOI  :  10.1016/j.jmaa.2017.07.013

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free