On initial boundary value problem with Dirichlet integralconditions for a hyperbolic equation with the Besseloperator

[摘要] We consider a mixed problem with Dirichlet and integralconditions for a second-order hyperbolic equation with the Besseloperator. The existence, uniqueness, and continuous dependence ofa strongly generalized solution are proved. The proof is based onan a priori estimate established in weighted Sobolev spaces andon the density of the range of the operator corresponding to theabstract formulation of the considered problem.

[学科分类] 应用数学