Uniqueness For Coefficient Identification In One-dimensional Parabolic Equations

Inverse problem of partial differential equation is a very important research subject in the field of applied mathematics.The problem has developed from the contact with some problems in numerous disciplines and engineering fields.In this paper we mainly talk about the problem of the unique identification of the coefficient in a parabolic partial differential equation,in terms of the inverse spectral theory of Sturm-Liouville differential operators.The works are given as follows:In the first chapter,we sum the research backgrounds,significance and advance of the identification of coefficients in a parabolic differential equation.In the second chapter,we give some relevant theorems of parabolic partial differ-ential equation and Sturm-Liouville differential operators,including the relationship of them.In the third chapter,we will talk about the problem of the unique identification of the coefficient in a one-dimensional parabolic partial differential equation.the solution of an initial-boundary value problem is observed at one internal point over a finite time interval.In terms of the inverse spectral theory of Sturm-Liouville differential operators we have the result that under the condition that one of the boundary value conditions is known,the coefficient on a subinterval is uniquely determined by such observation on a subinterval.