In this paper, we consider solving for a coefficient inverse problem in the parabolic equation. A new numerical method for the identification of the space-dependent coefficient is developed in a reproducing kernel space. The coefficients can be solved by a lower triangle linear system. Some numerical experiments are presented to show the efficiency of the proposed method.
Issue Section:
Conduction
1.
Duchateau
, P. C.
, 1995, “Monotonicity and Invertibility of Coefficients-to-Data Mapping for Parabolic Inverse Problems
,” SIAM J. Math. Anal.
0036-1410, 26
, pp. 1473
–1487
.2.
Shidfar
, A.
, and Azary
, H.
, 1997, “An Inverse Problem for a Nonlinear Diffusion Equation
,” Nonlinear Anal. Theory, Methods Appl.
0362-546X, 28
, pp. 589
–593
.3.
Cannon
, J. R.
, and Duchateau
, P. C.
, 1978, “Determination of Unknown Coefficients in Parabolic Operators From Overspecified Initial Boundary Data
,” ASME J. Heat Transfer
0022-1481, 100
, pp. 503
–507
.4.
Muzylev
, V.
, 1980, “Uniqueness Theorems for Some Converse Problems of Heat Conduction
,” USSR Comput. Math. Math. Phys.
0041-5553, 20
, pp. 120
–134
.5.
Alifanov
, O. M.
, Artyukhin
, E. A.
, and Rumyantsev
, S. V.
, 1988, Extreme Methods for Solving Ill-Posed Problems With Application to Inverse Heat Transfer Problems
, Nauka
, Moscow
, in Russian.6.
Fatullayev
, A. G.
, Can
, E.
, and Gasilov
, N.
, 2006, “Comparing Numerical Methods for Inverse Coefficient Problem in Parabolic Equation
,” Appl. Math. Comput.
0096-3003, 179
, pp. 567
–571
.7.
Chen
, Z.
, and Lin
, Y.
, 2008, “The Exact Solution of a Linear Integral Equation With Weakly Singular Kernel
,” J. Math. Anal. Appl.
0022-247X, 344
, pp. 726
–734
.8.
Cui
, M.
, and Lin
, Y.
, 2008, Nonlinear Numerical Analysis in the Reproducing Kernel Space
, Nova Science
, New York
.9.
Aronszajn
, N.
, 1950, “Theory of Reproducing Kernels
,” Trans. Am. Math. Soc.
0002-9947, 68
, pp. 337
–404
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.
