Inverse Problems Of Parabolic Equations With Dynamic Boundary Conditions

In this paper,we study the time reverse problem and inverse source problem of parabolic equations with dynamic boundary conditions.Firstly,we study the time reverse problem of the following equation:That is,to determine y(x,t0),t0∈(0,T)by observation data y(x,T).Then we consider an inverse source problem for the following equation:That is,to determine y by suitable observation f(x,t),x′∈ D′,0 < t < t0.In order to study the above inverse problem,we first establish Carleman estimates for the following equation:By selecting the appropriate weight function,we establish two kinds of the Carleman estimates and we can prove the uniqueness,stability for the time reverse problem and the uniqueness for the inverse source problem.