On solutions to initial boundary value problems for the Kawahara equation and its generalizations

The following presentation is devoted to the three problems for various modifications of the Kawahara equation. In the first part of the presentation we consider the large time decay of solutions of the initial boundary value problem for the damped Kawahara equation. We establish the well-posedness of such solution. The second part of the presentation is devoted to the investigation of the inverse problems for the generalized Kawahara equation with integral overdetermination and its linear analogue . The third part of the presentation is dedicated to the investigation of initial boundary value problems with different types of boundary conditions for a two-dimensional modification of the Kawahara equation. We establish the well-posedness and the large time decay of strong and weak solutions of the considered problem.