Parameter Estimation for Damped Sine-Gordon Equation with Neumann Boundary Condition

Abstract

In this thesis we study an identification problem for physical parameters associated with damped sine-Gordon equation with Neumann boundary conditions. The existence, uniqueness, and continuous dependence of weak solution of sine- Gordon equations are established. The method of transposition is used to prove the Gateaux differentiability of the solution map. The Gateax differential of the solution map is characterized. The optimal parameters are established. Frechet differentiability of the cost functional J is established. Computational algorithm and numerical results are presented.