Inverse Problems For A Fourth-order Parabolic Equation

In this paper,we consider inverse problems for a four-order parabolic equation.We first consider a time reverse problem for the following equation:That is,to determine y(x,t0)(0<t0<T)by observation data y(x,T).Then we consider an inverse source problem for the following equation:That is,to determine g by suitable observation y.To solve the inverse problems,we first derive Carleman estimates for the following equation:Then,by choosing the right weighting function,we establish the Carleman estimates and we can prove the uniqueness,stability for the time reverse problem and the uniqueness for the inverse source problem.