Search

In this article, the existence and uniqueness of generalized nonlinear impulsive evolution equation is derived. The proposed system is modeled with nonlinear perturbed force which changes after every impulse. The Banach contraction principle is applied to prove the existence and uniqueness of mild solution. The existence and uniqueness of classical solution is obtained by fixing the impulse and the conditions in which mild solution becomes classical solution also obtained. Finally an example is illustrated to the effectiveness of main results. [ABSTRACT FROM AUTHOR]

In this article, we study an inverse problem of reconstructing a space dependent coefficient in a generalized Korteweg-de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework and existence of a minimizer for the cost functional is established. Then we prove a stability estimate for retrieving the unknown coefficient in KdV equation with the upper bound of given measurements. The local uniqueness of the coefficient is also discussed. [ABSTRACT FROM AUTHOR]