A mollified method for the solution of the Cauchy problem for the convection-diffusion equation

Inverse Problems in Science and Engineering

Volumn 15, Issue 4, 2007, Pages 293-302

  Lesnic, D ^a   Wake, G C ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b MASSEY UNIVERSITY   (New Zealand)

Author keywords

Cauchy problem; Convection diffusion; Mollification method

Indexed keywords

DIFFUSION; PROBLEM SOLVING;

CAUCHY PROBLEMS; CONVECTION DIFFUSION EQUATION; MOLLIFICATION METHOD;

INVERSE PROBLEMS;

EID: 34248578631     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970600839002     Document Type: Article

References (21)

1. Smith, W.R., Wake, G.C., McIntosh, J.E.A., McIntosh, R.P., Pettigrew, M. and Kao, R., 1991, Mathematical analysis of perifusion data: models predicting elution concentration. American Journal of Physiology, 261, R247-R256.
2. de Mey, G., de Smet, S. and Driscart, M., 1991, Forced convection cooling of flat electronic substrates. In: C.A.Brebbia (Ed.) Boundary Element Technology VI(Southampton: Comput. Mech. Publ.), pp. 39-50.
3. Chatwin, P.C. and Allen, C.M., 1985, Mathematical models of dispersion in rivers and estuaries. Annual Review of Fluid Mechanics, 17, 119-149.
4. Smith, W.R., 1988, Entry and exit conditions for flow reactors. IMA Journal of Applied Mathematics, 41, 1-20.
5. Ginsberg, F., 1963, On the Cauchy problem for the one-dimensional heat equation. Mathematics of Computation, 17, 257-269.
6. Dinh Nho Hao, 1998, Methods for Inverse Heat Conduction Problems (Frankfurt: Peter Lang).
7. Smith, W.R. and Wake, G.C., 1990, Mathematical analysis: an inverse problem arising in convective-diffusive flow. IMA Journal of Applied Mathematics, 45, 225-231.
8. Losch, J.E., 1960, Tables of Higher Functions, 6th edn. (New York: McGraw-Hill).
9. Burggraf, R.O., 1964, An exact solution of the inverse problem in heat conduction theory and applications. ASME Journal of Heat Transfer, C86, 373-382.
10. Langford, D., 1966, New analytic solutions of the one-dimensional heat equation for temperature and heat flow both prescribed at the same fixed boundary (with applications to the phase change problem). Quarterly of Applied Mathematics, 24, 315-322.
11. Lesnic, D., 2005, The decomposition method for Cauchy advection-diffusion problems. Computers & Mathematics with Applications, 49, 525-537.
12. Jonas, P. and Louis, A.K., 2000, Approximate inverse for a one-dimensional inverse heat conduction problem. Inverse Problems, 16, 175-185.
13. Cannon, J.R., 1984, The One-Dimensional Heat Equation (Reading: Addison-Wesley).
14. Dinh Nho Hao and Gorenflo, R., 1991, A noncharacteristic Cauchy problem for the heat equation. Acta Applicandae Mathematicae, 24, 1-27.
15. Dinh Nho Hao, 1992, Regularization of a non-characteristic Cauchy problem for the heat equation. Mathematical Methods in the Applied Sciences, 15, 537-545.
16. Nikolskii, S.M., 1975, Approximation of Functions of Several Variables and Imbedding Theorems (Berlin: Springer-Verlag).
17. Murio, D.A., 1993, The Mollification Method and the Numerical Solution of Ill-Posed Problems (New York: Wiley).
18. Lesnic, D. and Elliott, L., 1999, The decomposition approach to inverse heat conduction. Journal of Mathematical Analysis and Applications, 232, 82-98.
19. Eiden, L., 1995, Numerical solution of the sideways heat equation by difference approximation in time. Inverse Problems, 11, 913-923.
20. Manselli, P. and Miller, K., 1980, Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side. Annali di Matematica Pura ed Applicata, 123, 161-183.
21. Erdelyi, A., 1953, Higher Transcedental Functions (New York: McGraw-Hill).