Energy decay estimates and infinite blow-up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source

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.