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Title: On the solution of inverse problems for generalized oxygen consumption (English)
Author: Constales, D.
Author: Kačur, J.
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 46
Issue: 2
Year: 2001
Pages: 145-155
Summary lang: English
Category: math
Summary: We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied. (English)
Keyword: oxygen consumption
Keyword: inverse problems
Keyword: automatic differentiation
MSC: 35K55
MSC: 35R30
MSC: 35R35
MSC: 49M15
MSC: 49N45
MSC: 49N50
MSC: 65M32
idZBL: Zbl 1059.65086
idMR: MR1818082
DOI: 10.1023/A:1013735806210
Date available: 2009-09-22T18:06:14Z
Last updated: 2020-07-02
Stable URL:
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Reference: [2] J. Crank: Free and Moving Boundary Problems.Oxford Science Publications, Clarendon Press, Oxford, 1984. Zbl 0547.35001, MR 0776227
Reference: [3] A. Griewank, G. F. Corliss: Automatic Differentiation of Algorithms: Theory, Implementation, and Application.SIAM, Philadelphia, 1991. MR 1143784
Reference: [4] A. C.  Hindmarsh: ODEPACK, a systematized collection of ODE solvers.In: Scientific Computing (R. S. Stapleman et al. (eds)), North-Holland, Amsterdam, 1983, pp. 55–64. MR 0751604
Reference: [5] L. R.  Petzold: Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations.SIAM J. Sci. Comput. 4 (1983), 136–148. Zbl 0518.65051, MR 0689694, 10.1137/0904010


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