Null Controllability Of N-Coupled Degenerate Parabolic Systems

In this thesis,the null controllability of the following n-coupled degenerate parabolic systems is studied:（?）where Q=（0,1）×（0,T）,T>0,the non empty subset ω=（α,β）（?）（0,1）,χ_ω is the characteristic function of the nonempty control region ω,diffusion coefficient a degenerates at x equals 0,and b_ij∈W_∞^2,1（Q）,c_ij∈L∞（Q）（1≤i,j≤n）,y_i,0∈L²ï¼ˆ0,1）（1≤i≤n）,h_k∈L²ï¼ˆQ）（1≤k ≤m ≤n）.This paper is divided into two cases to discuss.When the coefficient matrix B=(b_ij)n×n is a upper triangular matrix and C=(c_ij)n×n is a inclined upper triangular matrix,we select the appropriate energy weight function according to the structure of the equation.We firstly estimate a single degenerate parabolic equation.By the methods of summation and iteration,we get the Carleman estimation and observability inequalities of the conjugate problem corresponding to the original problem.Thus,we prove the null controllability of the original problem.When the coefficient matrix B is an identity matrix and C is a constant matrix,we deduce the null controllability of the problem under the Kalman rank condition.