Dynamics of multi-valued retarded p-Laplace equations driven by nonlinear colored noise

Author:

Wang Fengling12ORCID,Caraballo Tomás23ORCID,Li Yangrong1ORCID

Affiliation:

1. School of Mathematics and Statistics, Southwest University 1 , Chongqing 400715, China

2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla 2 , C/Tarfia s/n, 41012 Sevilla, Spain

3. Department of Mathematics, Wenzhou University 3 , Wenzhou, Zhejiang Province 325035, People's Republic of China

Abstract

This paper mainly considers the long-term behavior of p-Laplace equations with infinite delays driven by nonlinear colored noise. We firstly prove the existence of weak solutions to the equation, but the uniqueness of solutions cannot be guaranteed due to the lack of Lipschitz continuity conditions, and thus generate a multi-valued dynamical system. Moreover, the regularity of solutions is also proved. Then we prove the existence of a pullback attractor. Subsequently, the measurability of the pullback attractor and the multi-valued dynamical system are also proved.

Funder

China Scholar Council

Postgraduate Rwesearch and Innovate Projecto of Chongqing

Natural Science Fundation of China

Ministerio de Cienca e Innovación

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

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