IJAM, Volume 27, No. 3 (2014)

Abstract. In R. Almomani and H. Almefleh [1], the authors formulated the control problem of heat conduction problem with inverse direction of time and integral boundary conditions and they show the non-wellposedness of this problem. In H. Almefleh [2], the author reduced the solution of the control problem of the inhomogeneous heat equation to the homogeneous case. In H. Almefleh, R. Almomani [3] the authors established a priori estimate for the solution of quasi-inverse problem. In this paper we establish a new priori estimate for the same problem and the same order but with another weight function. The solution of our problem plays an important role in optimal control in heat conduction theory and in plasma physics, that is, in those problems where we have an integral restriction on a function.