Identifying a control function in two-dimensional parabolic inverse problems

Applied Mathematics and Computation

Volumn 143, Issue 2-3, 2003, Pages 375-391

  Dehghan, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Explicit techniques; Finite difference formula; Implicit methods; Inverse problem; Overspecified boundary data; Parabolic partial differential equations; Saulyev's schemes; Source control parameters

Indexed keywords

FINITE DIFFERENCE METHOD; FUNCTIONS; INVERSE PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS;

CONTROL FUNCTIONS;

COMPUTATIONAL METHODS;

EID: 0037507414     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00369-7     Document Type: Article

References (21)

1. Cannon J.R., Yin H.M. On a class of non-classical parabolic problems. J. Diff. Eq. 79:1989;266-288.
2. Cannon J.R., Yin H.M. Numerical solution of some parabolic inverse problems. Numer. Meth. Partial Diff. Eq. 2:1990;177-191.
3. Cannon J.R., Lin Y. Determination of parameter. p(t) in Holder classes for some semilinear parabolic equations Inv. Prob. 4:1988;595-606.
4. Cannon J.R., Lin Y. An inverse problem of finding a parameter in a semilinear heat equation. J. Math. Anal. Appl. 145(2):1990;470-484.
5. Cannon J.R., Lin Y. Determination of parameter. p(t) in some quasi-linear parabolic differential equations Inv. Prob. 4:1988;35-45.
6. Cannon J.R., van der Hoek J. Diffusion subject to the specification of mass. J. Math. Anal. Appl. 115:1986;527-536.
7. Cannon J.R., Lin Y., Wang S. Determination of source parameter in parabolic equations. Meccanica. 27:1992;85-94.
8. Day W.A. Extension of a property of the heat equation to linear thermoelasticity and other theories. Quart. Appl. Math. 40:1982;319-330.
9. Dehghan M. Fully implicit finite difference methods for two-dimensional diffusion with a non-local boundary condition. J. Comput. Appl. Math. 106:1999;255-269.
10. Gerald C.F. Applied Numerical Analysis. Fourth ed. 1989;Addison-Wesley, Reading, MA.
11. Lapidus L., Pinder G.F. Numerical solution of partial differential equations in science and engineering. 1982;Wiley, New York.
12. Macbain J.A., Bendar J.B. Existence and uniqueness properties for one-dimensional magnetotelluric inversion problem. J. Math. Phys. 27:1986;645-649.
13. Macbain J.A. Inversion theory for a parametrized diffusion problem. SIAM J. Appl. Math. 18:1987;1386-1391.
14. Mitchell A.R., Griffiths D.F. The Finite Difference Methods in Partial Differential Equations. 1980;T. Wiley.
15. Prilepko A.I., Orlovskii D.G. Determination of the evolution parameter of an equation and inverse problems of mathematical physics, part I. J. Diff. Eq. 21:1985;119-129. and part II 21 (1985) 694-701.
16. Prilepko A.I., Soloev V.V. Solvability of the inverse boundary value problem of finding a coefficient of a lower order term in a parabolic equation. Diff. Eq. 23(1):1987;136-143.
17. Rundell W. Determination of an unknown non-homogeneous term in a linear partial differential equation from overspecified boundary data. Appl. Anal. 10:1980;231-242.
18. Wang S. Numerical solutions of two inverse problems for identifying control parameters in 2-dimensional parabolic partial differential equations. Modern Developments in Numerical Simulation of Flow and Heat Transfer. HTP-vol. 194:1992;11-16.
19. Wang S., Lin Y. A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equation. Inv. Prob. 5:1989;631-640.
20. Dehghan M. A finite difference method for a non-local boundary value problem for two dimensional heat equation. Appl. Math. Comput. 112:2000;133-142.
21. Dehghan M. Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition. Nonlinear Anal. 48:2002;637-650.