SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CLASSICAL SOLUTION OF QUASI-INVERSE PROBLEM

Abstract

In [1], the authors established a priori estimate for the solution of quasi-inverse problem for different weight functions, and they established a priori estimate for a higher order of the same problem. In this paper we get the generalized a priori estimation for the uniqueness solution of quasiinverse problems and we get the sufficient conditions for the existence of classical solution of quasi-inverse problems, such a problem play an important role in optimal control theory. Many works were devoted to this problem and the control problem of heat conduction with inverse direction of time and integral boundary conditions [4, 5, 6, 7, 8, 9]. AMS Subject Classification: 35R30