Regularization algorithm within two parameters for the identification of the heat conduction coefficient in the parabolic equation

• Published in: Mathematical and computer modelling Vol. 57; no. 7-8; pp. 1990 - 1998
• Main Authors: Hinestroza G., Doris, Peralta, Jenifer, Olivar, Luis Eduardo
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2013
• Subjects: Adjoint problems; Coefficient identification; Ill-posed problems; Inverse problems; Parabolic equations; Regularization methods; Sensitivity equations; Parabolic equations; Ill-posed problems; Inverse problems; Coefficient identification; Regularization methods; Adjoint problems; Sensitivity equations
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2012.02.002

Our approach is based in a new and promising regularization algorithm with an approximation process by a minimization of especial functional that depends on two regularization parameters for the identification of the nonlinear heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient as in conventional Tikhonov algorithms but the other is associated with the calculated solution. Numerical examples are presented to show how the method works.