×

zbMATH — the first resource for mathematics

Numerical identification of a coefficient in a parabolic quasilinear equation. (English) Zbl 0574.65136
An identification problem of a nonlinear function in a quasilinear equation of parabolic type arising in mathematical modelling of gas chromatography is considered. The identification is formulated as an optimal control problem, whose existence is discussed. A method for the numerical solution of the optimal control problem is described in details. In the method a finite-difference approximation of the state equation is used and the obtained nonlinear optimization problem is solved using a modification of the conjugate gradient algorithm. The results of a numerical example are presented.
Reviewer: K.Malanowski

MSC:
65Z05 Applications to the sciences
65K10 Numerical optimization and variational techniques
35K20 Initial-boundary value problems for second-order parabolic equations
35R30 Inverse problems for PDEs
49J20 Existence theories for optimal control problems involving partial differential equations
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] D. R. Richtmyer K. W. Morton: Difference methods for initial value problem. Interscience Publishers, a division of John Wiley & Sons, 1967. · Zbl 0155.47502
[2] J. L. Lions: Controle optimal de systèmes gouvernés par des équations aux dérivées partielles. Paris, Dunod 1968. · Zbl 0179.41801
[3] J. H. Mufti: Computational methods in optimal control problems. (Lecture Notes in Operations Research and Mathematical Systems, n. 27); Berlin-Heidelberg-New York, Springer Verlag 1979.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.