On the Well-Posedness of Mild Solutions to Certain Nonlinear Wave Equations

Abstract

We are devoted 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.