A coupled system of Laplacian and bi-Laplacian equations with nonlinear dampings and source terms of variable-exponents nonlinearities: Existence, uniqueness, blow-up and a large-time asymptotic behavior

AIMS Mathematics

article

Salim A. Messaoudi¹  Mohammad M. Al-Gharabli²  Adel M. Al-Mahdi²  Mohammed A. Al-Osta³ 

[1] Department of Mathematics and Statistics, University of Sharjah;The Preparatory Year Program, King Fahd University of Petroleum & Minerals;The Interdisciplinary Research Center for Construction and Building Materials, King Fahd University of Petroleum and Minerals;Department of Civil Engineering, King Fahd University of Petroleum and Minerals

关键词: biharmonic equations;    blow-up;    coupled system;    global existence;    variable exponent;    stability;   

DOI  :  10.3934/math.2023400

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we consider a coupled system of Laplacian and bi-Laplacian equations with nonlinear dampings and source terms of variable-exponents nonlinearities. This system is supplemented with initial and mixed boundary conditions. First, we establish the existence and uniqueness results of a weak solution, under suitable assumptions on the variable exponents. Second, we show that the solutions with positive-initial energy blow-up in a finite time. Finally, we establish the global existence as well as the energy decay results of the solutions, using the stable-set and the multiplier methods, under appropriate conditions on the variable exponents and the initial data.

【 授权许可】

CC BY