Semilinear Wave Inequalities with Double Damping and Potential Terms on Riemannian Manifolds

Jleli M. Ruzhansky M. Samet B. Torebek B.T.
October 2025 Springer

Journal of Geometric Analysis
2025 #35 Issue 10

We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function V depending on the space variable in front of the power nonlinearity and an inhomogeneous term W depending on both time and space variables. Namely, we establish sufficient conditions for the nonexistence of weak solutions in both cases: W≡0 and W≢0. The obtained conditions depend on the parameters of the problem as well as the geometry of the manifold. Some special cases of manifolds, and of V and W are discussed in detail.

critical exponent , nonexistence , Ricci curvature , Riemannian manifold , Semilinear wave inequality

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Department of Mathematics, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Department of Mathematics
Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling

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