Unique Continuation Property Of Solutions To Cauchy Problem For Two Kinds Of Partial Differential Equations

This paper mainly discusses the unique continuation of the solutions of the Cauchy problem for two kinds of nonlinear partial differential equations.Unique continuation property in integrable systems and control theory.So far,the unique continuation of the solutions of the nonlinear partial differential equations has been studied widely.This paper uses the Paley-Weiner theorem in Fourier analysis to prove unique continuation property of the solution of the initial value problem for a class of Kawahara-Burgers and KdV-Burgers equations.The full text structure is as follows:In the first chapter,we briefly review the progress of the research on the unique continuation property of partial differential equations.The second chapter gives relevant basic knowledge and basic conclusions.In the third chapter,we study the unique continuation property of solution for Cauchy problem for a class of Kawahara-Burgers equations.In the fourth chapter,we introduce the unique continuation property of solution for KdV-Burgers equation.