Existence of Random Attractors for a Stochastic Strongly Damped Plate Equations with Multiplicative Noise
Mohamed Y. A. Bakhet *
School of Mathematics, University of Juba, Juba, Central Equaturia, South Sudan.
Makur Makuac Chinor
School of Mathematics, University of Juba, Juba, Central Equaturia, South Sudan.
Abdelmajid Ali Dafallah
Department of Mathematics, Faculty of Petroleum and Hydrology Engineering, Alsalam University, Almugled, Sudan.
Fadlallah Mustafa Mosa
Department of Mathematics and Physics, Faculty of Education University of Kassala, Kassala, Sudan.
Paride O. Lolika
Department of Mathematics, University of Juba, Juba, Central Equaturia, South Sudan.
Sulieman A. S. Jomah
Department of Mathematics, University of Juba, Juba, Central Equaturia, South Sudan.
Ahmed Eshag Mohamed
Department of Mathematics, Faculty of Pure and Applied Sciences, International University of Africa, Khartoum, Sudan.
*Author to whom correspondence should be addressed.
Abstract
In this article, we study the asymptotic dynamics of a stochastic strongly damped plate system with homogeneous Neumann boundary conditions and multiplicative noise. First, we investigate the existence and uniqueness of solutions in infinite-dimensional dynamical systems using the notion of mild solutions, and then we examine the presence of a bounded absorbing set. Finally, we investigate the asymptotic compactness by using the decomposition technique to prove the existence of a random attractor.
Keywords: Plate equations, random attractors, strongly damped, dynamical systems