Linear recursive schemes associated with the nonlinear wave equation involving Bessel's operator

Abstract

We prove the existence and uniqueness of a weak solution of a semilinear wave equation involving Bessel's operator, the nonlinear term being in the form f( r, t, u, ▿ u), while the boundary condition at r = 0 takes the weak form ▪. In the proof, the Faedo-Galerkin method associated with a linear recursive scheme in appropriate Sobolev spaces with weight is used.