Abstract:
The Wave equation is second order linear partial differential equations that concerns
different physical phenomena. The Cauchy problem for wave equation is to find the
solution of the wave equation subject to initial conditions. Thus in this thesis we studies
the existence, uniqueness and stability the Cauchy problem for wave equations. We find
that the solution of the Cauchy problem for one dimensional wave equation exist and
continuously depends on initial conditions. We examine the solution using analytical
method and computational method. Special we find the solution by separation of the
variable method, d’Alembert formula, Mathematica software and computer C++
programming.
