An initial-boundary value problem for a nonlinear wave equation in an \(n\)-dimensional rectangular domain (Q5951138)

Using the generalized Fourier method, the author reduces the initial-boundary value problem for a nonlinear wave equation \(u_{tt}=\triangle u+f(t,x_{1},x_{2},\dots ,x_{n},u,u_{t},u_{x_{1}},\dots ,u_{x_{n}}),\) and Dirichlet conditions on the boundary of the unit square to a system of integral equations. He proves the existence and uniqueness of the generalized solution of the problem for sufficiently small \(t.\)