| We study a model of a nonlinear stretched string. Various initial and boundary value problems of the Carrier-Narasimha model with distributed damping in the interior of the spatial domain have been extensively studied in the literature. In this thesis, damping is shifted to the boundary and we show that for small enough initial data, the resulting equations with boundary dissipation has a unique smooth solution. The physical motivation for this comes from a variety of applications where it is easier to achieve dissipation on the boundary rather than in the interior. However, the mathematical analysis involved in boundary stabilization is usually more demanding, due to the unbounded nature of boundary operators. We approach this problem by obtaining a local solution through the Contraction Mapping Theorem and then using Energy Methods and Multipliers to provide an apriori bound of the solution. This extends the local solution to a global one. Stability of the solution is also shown. |
