Unique Continuation For Several Kinds Of Equations

This is a remark on the unique continuation problem for several kinds of differential equation, via the methods of Carleman inequality, Fourier series, expansion in series, reducing the parabolic equation to elliptic equation and so on. This paper describes the unique continuation property of parabolic operater, the neighborhood of angle, the parabolic equation on the non-cylinder domain and sencond order of parabolic equation with nonsmooth coefficients. And then we introduce the LP Carleman inequality, doubling property of parabolic equation with nonsmooth coefficients, and the control of heat equation on the oscillation in low dimension flow.