@article{Messaoudi2023, 
author = {Salim A. Messaoudi and Mohammad M. Al-Gharabli and Adel M. Al-Mahdi and Mohammed A. Al-Osta},
title = {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},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {7933-7966},
keywords = {biharmonic equations, blow-up, coupled system, global existence, variable exponent, stability},
url = {https://www.sciopen.com/article/10.3934/math.2023400},
doi = {10.3934/math.2023400},
abstract = {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.}
}