Stability Study Of Coefficient Identification Problem Of Coupled Schr?dinger Equations

The coupled Schrodinger equations are derived from a variety of practical problems and have practical applications in many disciplines,such as physics,biology,chemistry and economics.Coefficient identification problem is a classic inverse problem.Identify ing the coefficients in the system with additional observations can be used to study the properties of the system.Carleman estimates play a pivotal role in the coefficient identifi cation problem of inferring global information from partial information and are effective tools for studying the stability of inverse problemsThis thesis mainly studies the stability of two types of coefficients identification problems for the coupled Schrodinger equations under two kinds of observation con ditions.We establish the Carleman estimates of the coupled Schrodinger.Then,with the established Carleman estimates,the Lipschitz stability of identifying the coefficient matrix A in the coupled Schrodinger equations i???_tu+?u+Au = 0 is studied.The results of the study include:First,ajj?x??1?j?n?in the matrix A are unknown a_ij?x??i?j?are known,and a_ijsatisfy certain priori conditions.The conditional sta bility of identifying diag?A?(A =(a_ij)n×n)is obtained with the additional observation data???u/???v|S+×?0,t?or u|?×?0,T?,respectively.Second,a_ij?x??1?i,j?n?in matrix A are unknown and a_ij satisfy certain priori conditions.The conditional stability of identi fying A ?(a_ij)n×n is obtained with the additional observation condition x ?S+????,????na_ij???=a????1<i<n?or x ??????,????n???a'???u???=a'????1<i<n?,resnectively.