Sınırlı aralıklardaki Korteweg-de Vries denklemi

In this thesis, we study existence, uniqueness and stability results for the solutions of initial-boundary value problems for the Korteweg-de Vries equation on bounded domains. First, we give a proof of the existence and uniqueness of weak solutions in the case of periodic boundary conditions. We also give a proof for the existence of an absorbing set in the Sobolev space H^2. Then, we give a proof of the existence and uniqueness of regular solutions of a non-periodic initial-boundary value problem for the Korteweg-de Vries equation. In the non-periodic case, the exponential decay of solutions for small enough initial data is also shown.