… In this work we consider an initial-boundary value problem for the one-dimensional wave
equation. We prove the uniqueness of the solution and show that the solution coincides with
the wave potential. … Unlike elliptic and parabolic cases, where we obtained non-local
boundary conditions for the corresponding volume potentials, and some other nonclassic
non-local boundary initial boundary value problems of hyperbolic equations (see, for
example, [6, 7]) we get a local initial boundary value problem for the wave potential. …

For several of the wave phenomena that we might see or experience around us, we can
derive the partial differential equations that govern their behavior. Even though the primary
physical factors that give rise to these wave phenomena differ, by examining these partial
differential equations it is possible to find some common form for them. Vibration and wave
propagation phenomena are governed by partial differential equations known as wave
equations. Our goal in this thesis is to study initial and initial-boundaiy value problems …