On inverse problems for the generalized Kawahara equation with integral overdetermination

Abstract

In the following paper we study the inverse problems for the generalized Kawahara equation and its linearized analog in a bounded domain with integral overdetermination. As the control function we consider either a special form of the right-hand side of the equation or the value of the derivative of the solution on one of the boundaries. In order to achieve the controllability of the generalized Kawahara equation we impose smallness conditions on either the time interval or the input data. Those restrictions are absent in linear case.