On the well-posedness of mild solutions to certain nonlinear wave equations

We aredevoted to the study of the Cauchy problem for Love equation. We establish the existence and uniqueness of the solution under different conditions imposed on the nonlinear source function. We analyze the continuous dependence of the solution with respect to the parameters involved in the equation. Additionally, in this paper, we also shown that the solution to the Love equation converges to the solution of the wave equation.