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This paper deals with the energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source term under null Dirichlet boundary condition. By constructing a new family of potential wells, together with logarithmic Sobolev inequality and perturbation energy technique, we establish sufficient conditions to guarantee the solution exists globally or occurs infinite blow‐up and derive the polynomial or exponential energy decay estimates under some appropriate conditions.

In this paper, we introduce a new class of (p, h)-convex functions which generalize P-functions and convex, h, p, s-convex, Godunova-Levin functions, and we give some properties of the functions. Moreover, we establish the corresponding Schur, Jensen, and Hadamard types of inequalities.

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