A mixed problem for a Boussinesq hyperbolic equation with integral condition

TL;DR

This paper investigates a hyperbolic Boussinesq equation with mixed local and non-local boundary conditions, establishing the existence and uniqueness of strong solutions through functional analysis techniques.

Contribution

It introduces a novel approach to solving a Boussinesq hyperbolic problem with integral conditions, proving well-posedness using a priori estimates and operator density arguments.

Findings

Existence of strong solutions is proven.

Uniqueness of solutions is established.

The method applies functional analysis to mixed boundary conditions.

Abstract

A hyperbolic problem wich combines a classical(Dirichlet) and a non-local contraint is considered.The existence and uniqueness of strong solutions are proved,we use a functionnal analysis method based on a priori estimate and on the density of the range of the operator generated by the considered problem.