About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Constales, D. ; Kačur, J.
On the solution of inverse problems for generalized oxygen consumption. (English). Applications of Mathematics, vol. 46 (2001), issue 2, pp. 145-155
MSC: 35K55, 35R30, 35R35, 49M15, 49N45, 49N50, 65M32 | MR 1818082 | Zbl 1059.65086 | DOI: 10.1023/A:1013735806210
Keywords:
oxygen consumption; inverse problems; automatic differentiation
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.
References:
[1] H. W. Alt, S. Luckhaus: Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983), 311–341. DOI 10.1007/BF01176474 | MR 0706391
[2] J. Crank: Free and Moving Boundary Problems. Oxford Science Publications, Clarendon Press, Oxford, 1984. MR 0776227 | Zbl 0547.35001
[3] A. Griewank, G. F. Corliss: Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, 1991. MR 1143784
[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
[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. DOI 10.1137/0904010 | MR 0689694 | Zbl 0518.65051
Partner of
EuDML logo