On the solution of inverse problems for generalized oxygen consumption
Applications of Mathematics (2001)
- Volume: 46, Issue: 2, page 145-155
- ISSN: 0862-7940
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topConstales, Denis, and Kačur, Jozef. "On the solution of inverse problems for generalized oxygen consumption." Applications of Mathematics 46.2 (2001): 145-155. <http://eudml.org/doc/33080>.
@article{Constales2001,
abstract = {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.},
author = {Constales, Denis, Kačur, Jozef},
journal = {Applications of Mathematics},
keywords = {oxygen consumption; inverse problems; automatic differentiation; oxygen consumption; inverse problems; automatic differentiation},
language = {eng},
number = {2},
pages = {145-155},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the solution of inverse problems for generalized oxygen consumption},
url = {http://eudml.org/doc/33080},
volume = {46},
year = {2001},
}
TY - JOUR
AU - Constales, Denis
AU - Kačur, Jozef
TI - On the solution of inverse problems for generalized oxygen consumption
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 2
SP - 145
EP - 155
AB - 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.
LA - eng
KW - oxygen consumption; inverse problems; automatic differentiation; oxygen consumption; inverse problems; automatic differentiation
UR - http://eudml.org/doc/33080
ER -
References
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- Automatic Differentiation of Algorithms: Theory, Implementation, and Application, SIAM, Philadelphia, 1991. (1991) MR1143784
- ODEPACK, a systematized collection of ODE solvers, In: Scientific Computing (R. S. Stapleman et al. (eds)), North-Holland, Amsterdam, 1983, pp. 55–64. (1983) MR0751604
- 10.1137/0904010, SIAM J. Sci. Comput. 4 (1983), 136–148. (1983) Zbl0518.65051MR0689694DOI10.1137/0904010
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