Inverse Problems For Fourth-order Stochastic Parabolic Equations

In this paper,two kinds of inverse problems for the fourth-order stochastic parabolic equations are concerned.First,we consider the time reverse problem for the following equation:(?)That is,to determine the value of y(x,t0)(0<t0<T)by observing the value of y(x,T),Next,we consider the time reverse problem for the equation as follows:(?)where g = g1(t)g2(x),and g2(x)is known,hopefully to determine the values of g1(t)and y(x,t0)(0<t0<T)by observilg the value of y(x,T).In order to consider inverse problems,we need choose appropriate weight func-tions to establish Carleman estimates for the two equations.Then,we can prove the uniqueness and stability for the time reverse problems.