On a nonlinear wave equation involving the term −∂∂x(μ(x,t,u,‖ux‖2)ux): Linear approximation and asymptotic expansion of solution in many small parameters

In this paper, we consider the following nonlinear Kirchhoff wave equation equation(1){utt−∂∂x(μ(x,t,u,‖ux‖2)ux)=f(x,t,u,ux,ut),0