A Unique Continuation Result For A Multidimensional Fourth-order Parabolic Equation

In this paper,we consider a unique continuation problem for a Cauchy problem of a multidimensional fourth-order parabolic equations.we consider the following Cauchy problem:(?)Where Ω∈Rn,n≥2 is a bounded domain,and Γ(?)Ω is an open subset of the boundary.Specifically,we will determine u in a subset of Ω ×(0,T)by f,gi(1≤i ≤5).To do this,we first establish a new Carleman estimates for the equation by choosing suit-able weight function.Then,by using this Carleman estimate,we obtain a Horder stability result for the above Cauchy problem.And the unique continuation results is also implied by the stability for the Cauchy problem.