This work studies the global behavior of solutions for a system of (p(x), q(x))- Kirchhoff-type equations. We prove the global existence of solutions, and next, by constructing suitable auxiliary functionals, the general decay of solutions has been confirmed when the exponents satisfy appropriate conditions. Also, under suitable conditions on data, we establish the finite time blow-up of solutions with negative initial energy. Our results extend and improve many earlier results in the literature.

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