Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 181 -- 203

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This work is licensed under a Creative Commons Attribution 4.0 International License.

DYNAMICS OF THE STOCHASTIC WAVE EQUATIONS WITH DEGENERATE MEMORY EFFECTS ON BOUNDED DOMAIN

Abdelmajid Ali Dafallah, Fadlallah Mustafa Mosa, Mohamed Y. A. Bakhet and Eshag Mohamed Ahmed

Abstract. In this work, we consider the behavior of long-time dynamics of a random dynamical system generated wave equations with degenerate memory and additive noise, on bounded domain U, with Dirichlet boundary condition, and nonlinear term f(u) with critical growth conditions, then we establish the existence of a random attractor.

2020 Mathematics Subject Classification: 37L55; 35R60; 35B40; 35B41; 35B45.
Keywords: Stochastic Wave Equations; Degenerate Memory; Random Dynamical System; Random Attractor.

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Abdelmajid A. D.
Faculty of Petroleum and Hydrology Engineering, Alsalam University, Almugled, Sudan.
majid-dafallah@yahoo.com

Fadlallah M. M.
Department of Mathematics and physics, Faculty of Education University of Kassala Kassala, Sudan.
e-mail: fadlmushan@hotmail.com

Mohamed Y. A. Bakhet
Department of Mathematics, College of Education Rumbek University of Science and Technology Rumbek, South Sudan.
e-mail: myabakhet@hotmail.com

Ahmed E. M.
Department of Mathematics, Faculty of Pure and Applied Sciences, International University of Africa, Khartoum, Sudan.
e-mail: ahmedesag@gmail.com

http://www.utgjiu.ro/math/sma