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Investigates wave equation stability in variable exponent spaces, suggesting significant implications on solution behavior.
This paper is devoted to the study of a nonlinear viscoelastic wave equation featuring a logarithmic feedback nonlinearity with a variable exponent [Formula: see text]. We first prove the local and global well-posedness of solutions using the Galerkin approximation scheme, together with uniform a priori estimates and the Lions-Aubin compactness theorem. We then derive decay estimates by introducing a suitably designed Lyapunov functional.
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Otmani et al. (2026) studied this question.
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