Aiming at the initialboundary value problem of a class of wave equation with k Laplace operator and multiple nonlinear source terms, Galerkin approximation method is applied to proving the existence of global weak solutions of the equation.This kind of wave equation improves the wave equation with a single nonlinear source term.Because the wave equation introduces k Laplace operator term and multiple nonlinear source terms, it makes the structure of the wave equation more refined and practical.Firstly, the definition of weak solutions of the wave equation is given, and then some necessary functionals are defined.The properties of these functionals are proved by using limit and derivative, and the invariant set of solutions of the wave equation under certain conditions is proved.Finally, the Galerkin approximation method is used to construct the approximate solution of the wave equation by means of the basic solution system of the characteristic equation.The existence of the global weak solution of the equation is obtained by analyzing the convergence of the approximate solution.