Inverse Problems for the Generalized Kawahara Equation

Abstract In this paper we study the inverse problems for the generalized form of Kawahara equation as well as 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.