Coupled System of Nonlinear Hyperbolic Equations with Variable-Exponents: Global Existence and Stability

Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents

“…This work generalizes many other works in the literature. In particular, we obtain the results of [9,23], if α(•) = β(•).…”

“…Concerning coupled systems of hyperbolic equations with variable exponents, we mention the work of Bouhoufani and Hamchi [9], where they proved the existence of a global weak solution and established decay estimates of the energy depending on the variable exponents. Messaoudi and Talahmeh [24] considered a system of wave equations, with damping and source terms of variable-exponent nonlinearities, and proved a blow-up result for solutions with negative initial energy.…”

Global existence and stability of the wave equation with boundary variable damping

“…In 2022, Messaoudi and Zahri [16] proved that a weak solution of a damped wave equation with variable-exponent nonlinearities decay exponentially or polynomially depending on the range of the variable exponent. For more studies in this direction, we refer the readers to [2,4,15,20].…”