A wave equation associated with mixed nonhomogeneous conditions: global existence and asymptotic expansion of solutions (Q875263)

An initial boundary value problem for the linear wave equation is considered. The unknown function \(u(x , t)\) and the unknown BV function \(P(t)\) are asked to satisfy a nonlinear integral equation. Under certain regularity conditions one proves the global existence and uniqueness of a weak solution \(( u, P)\). For some special values of parameters which simplify consistently the integral condition transforming it into a linear one, a study of the asymptotic behaviour of the solution \((u, P)\) is done.