| 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:
|
http://hdl.handle.net/10338.dmlcz/134461 |
| . |
| Reference:
|
[1] H. W. Alt, S. Luckhaus: Quasilinear elliptic-parabolic differential equations.Math. Z. 183 (1983), 311–341. MR 0706391, 10.1007/BF01176474 |
| 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 |
| . |
