Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 11, Issue 1-2, 2004, Pages 181-199

  Azari, Hossein ^a   Allegretto, Walter ^b   Lin, Yanping ^b   Zhang, Shuhua ^c  

^a INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

^b UNIVERSITY OF ALBERTA   (Canada)

^c TIANJIN UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Convergence; Inverse problem; Maximum principle; Numerical method

Indexed keywords

EID: 4544288635     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (14)

1. Hossein Azari, Numerical procedures for the determination of an unknown coefficient in parabolic differential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 9 (2002), no. 4, 555-573. MR 2003h:35275
2. J. R. Cannon, Determination of an unknown coefficient in a parabolic differential equation, Duke Math. J., 30 (1963), 313-323.
3. J. R. Cannon, Yanping Lin, and Shingmin Wang, Determination of source parameter in parabolic equation, Meccanica, 27 (1992), 85-94.
4. J. R. Cannon, Yanping Lin, and Shuzhan Xu, Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations, Inverse Problems, 10 (1994), no. 2, 227-243. MR 96a:65125
5. J. R. Cannon and W. Rundell, Recovering a time dependent coefficient in a parabolic differential equation, J. Math. Anal. Appl., 160 (1991), no. 2, 572-582. MR 92g:35227
6. J. R. Cannon and Hong-Ming Yin, Numerical solutions of some parabolic inverse problems, Numer. Methods Partial Differential Equations, 6 (1990), no. 2, 177-191. MR 92g:65205
7. Jr. B. F. Jones, The determination of a coefficient in a parabolic differential equation, I. Existence and uniqueness, J. Math. Mech., 11 (1962), 907-918.
8. -, The determination of a coefficient in a parabolic equation, Duke Math. J., 30 (1963), 313-324.
9. -, Various methods for finding unknown coefficients in parabolic differential equations, Comm. Pure Appl. Math., XVI (1963), 33-44.
10. Yanping Lin, Analytical and numerical solutions for a class of nonlocal nonlinear parabolic differential equations, SIAM J. Math. Anal., 25 (1994), no. 6, 1577-1594. MR 95i:35167
11. Yanping Lin and R. J. Tait, Finite-difference approximations for a class of nonlocal parabolic boundary value problems, J. Comput. Appl. Math., 47 (1993), no. 3, 335-350. MR 94j:65128
12. Yanping Lin, Shuzhan Xu, and Hong-Ming Yin, Finite difference approximations for a class of non-local parabolic equations, Internat. J. Math. Math. Sci., 20 (1997), no. 1, 147-163. MR 97i:65155
13. M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Springer-Verlag, 1984.
14. Hong-Ming Yin, Solvability of a class of parabolic inverse problems, Adv. Differential Equations, 1 (1996), no. 6, 1005-1023. MR 97h:35236