Abstract:
In this paper, we consider the non-homogeneous wave equation generated by the Bessel operator. We prove
the existence and uniqueness of the solution of the non-homogeneous wave equation generated by the
Bessel operator. The representation of the solution is given. We obtained a priori estimates in Sobolev type
space. This problem was firstly considered in the work of M. Assal [1] in the setting of Bessel-Kingman
hypergroups. The technique used in [1] is based on the convolution theorem and related estimates. Here,
we use a different approach. We study the problem from the point of the Sobolev spaces. Namely, the
conventional Hankel transform and Parseval formula are widely applied by taking into account that between
the Hankel transformation and the Bessel differential operator there is a commutation formula [2].
