Geodesic
Numerical identification of a coefficient in a parabolic quasilinear equation
Applications of Mathematics, Tome 30 (1985) no. 2, pp. 110-125
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of the boundary-value problem, existence of the solution of the optimal control problem).
In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of the boundary-value problem, existence of the solution of the optimal control problem).
DOI : 10.21136/AM.1985.104132
Classification : 35K20, 35R30, 49D07, 49J20, 65K10, 65Z05, 93B30
Keywords: quasilinear parabolic equation; identification; gas chromatography; optimal control; numerical example 
@article{10_21136_AM_1985_104132,
     author = {Neumann, Jan},
     title = {Numerical identification of a coefficient in a parabolic quasilinear equation},
     journal = {Applications of Mathematics},
     pages = {110--125},
     year = {1985},
     volume = {30},
     number = {2},
     doi = {10.21136/AM.1985.104132},
     mrnumber = {0778982},
     zbl = {0574.65136},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1985.104132/}
}
TY  - JOUR
AU  - Neumann, Jan
TI  - Numerical identification of a coefficient in a parabolic quasilinear equation
JO  - Applications of Mathematics
PY  - 1985
SP  - 110
EP  - 125
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1985.104132/
DO  - 10.21136/AM.1985.104132
LA  - en
ID  - 10_21136_AM_1985_104132
ER  - 
%0 Journal Article
%A Neumann, Jan
%T Numerical identification of a coefficient in a parabolic quasilinear equation
%J Applications of Mathematics
%D 1985
%P 110-125
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1985.104132/
%R 10.21136/AM.1985.104132
%G en
%F 10_21136_AM_1985_104132
Neumann, Jan. Numerical identification of a coefficient in a parabolic quasilinear equation. Applications of Mathematics, Tome 30 (1985) no. 2, pp. 110-125. doi: 10.21136/AM.1985.104132

[1] D. R. Richtmyer K. W. Morton: Difference methods for initial value problem. Interscience Publishers, a division of John Wiley & Sons, 1967. | MR

[2] J. L. Lions: Controle optimal de systèmes gouvernés par des équations aux dérivées partielles. Paris, Dunod 1968. | MR | Zbl

[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.

Cité par Sources :