The global existence of one type of nonlinear Kirchhoff string equation (Q1432863)

This paper deals with the global existence and uniqueness of the solution to the mixed (initial-boundary value) problem of the nonlinear Kirchhoff string equation in a cylinder. The equation contains the damping term \(| u_t|^{m-1}u_t\) and the source term \(| u|^{p-1}u\). Imposing suitable conditions on \(p> 1\) and \(m> 1\) the author proves the existence of a unique solution of the above-mentioned mixed problem for \(t\geq 0\). The proof is based on the energy method.