Global solvability of the Cauchy characteristic problem for one class of nonlinear second order hyperbolic systems (Q624643)

The solution of the system \(\frac{\partial ^2}{\partial t^2}u_{i}-\Delta u_{i}+\lambda \frac{\partial }{\partial u_{i}}G(u_1, u_2,\dots u_{N})=F_{i}(x,t)\), \(i=1,2,\dots N\) in \(\{[x,t]\in \mathbb {R}^{n+1}\: | x| <t<T\}\) satisfying the conditions \(u_{i}(x,| x| )=0,\) where \(n,N\geq 2\) is discussed. Under certain assumptions on the function \(G\) the authors prove existence and uniqueness of the strong generalized solution of the problem.