New a Priori Estimations of the Solution of Quasi-Inverse Problem

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.

Higher Order Estimation of the Solution of Quasi-Inverse Problem

“…A priori estimates for the solution of a quasi-inverse problem with different weight functions were proposed there. Here we establish a priori estimate of higher order for the above problem (1). We start from the following identity:…”

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In [1,2] the authors established a priori estimate for the solution of quasi-inverse problem of the same order but for different weight functions. In this paper we establish a priori estimate for a higher order of the same problem, such a problem play an important role in optimal control theory.

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New a Priori Estimations of the Solution of Quasi-Inverse Problem

“…H. Almefleh, R. Almomani [3] but with another weight function. By scalar multiplication of (1) in L 2 (Q τ ) by the function…”