Asymptotic stability for Kirchhoff systems in variable exponent Sobolev spaces

We deal with the question of global and local asymptotic stabilities, as time tends to infinity, of solutions of dissipative anisotropic Kirchhoff systems, governed by the p(x)-Laplacian operator, in the framework of the variable exponent Sobolev spaces. Concrete applications are presented in special subcases of the external force f and the distributed damping Q involved in the systems.

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