×

zbMATH — the first resource for mathematics

On an invariant set in the heat conductivity problem with time lag. (English) Zbl 1304.35325
Summary: The problems of weak and strong invariance of a constant multivalued mapping with respect to the heat conductivity equation with time lag are studied. Sufficient conditions of weak and strong invariance of a given multivalued mapping are obtained.
MSC:
35K20 Initial-boundary value problems for second-order parabolic equations
35Q93 PDEs in connection with control and optimization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Guseń≠nov, Kh. G.; Ushakov, V. N., Strongly and weakly invariant sets with respect to a differential inclusion, Doklady Akademii Nauk USSR, 303, 794-796, (1988)
[2] Aubin, J.-P., A survey of viability theory, SIAM Journal on Control and Optimization, 28, 4, 749-788, (1990) · Zbl 0714.49021
[3] Kurzhanski, A. B.; Filippova, T. F., On the description of the set of viable trajctories of a control system, Differential Equations, 23, 8, 1303-1315, (1987) · Zbl 0637.49018
[4] Fazilov, A. Z.; Ibragimov, U. M., On the Strong Invariant Sets of Linear Control System. On the Strong Invariant Sets of Linear Control System, Mathematics, Informatics, and Physics, 4, (2003), Science and Education of South Kazakhstan
[5] Haddad, G., Monotone trajectories of differential inclusions and functional-differential inclusions with memory, Israel Journal of Mathematics, 39, 1-2, 83-100, (1981) · Zbl 0462.34048
[6] Borzabadi, A. H.; Kamyad, A. V.; Farahi, M. H., Optimal control of the heat equation in an inhomogeneous body, Journal of Applied Mathematics and Computing, 15, 1-2, 127-146, (2004) · Zbl 1048.49016
[7] Fattorini, H. O., The maximum principle for control systems described by linear parabolic equations, Journal of Mathematical Analysis and Applications, 259, 2, 630-651, (2001) · Zbl 1078.49505
[8] Islamov, G. G.; Kogan, Yu. V., The differential-difference problem of control of diffuzion process, Vestnik Udmurtskogo Universiteta, 303, 1, 121-126, (2008)
[9] Tukhtasinov, M.; Ibragimov, U., Sets invariant under an integral constraint on controls, Russian Mathematics, 55, 8, 59-65, (2011) · Zbl 1227.93058
[10] Tukhtasinov, M.; Ibragimov, U., Invariant sets with respect to the system with lag, Reports of Academy of Sciences of Republic of Uzbekistan, 15, 12-15, (2011)
[11] Alimov, Sh., On the null-controllability of the heat exchange process, Eurasian Mathematical Journal, 2, 5-19, (2011) · Zbl 1253.93010
[12] Albeverio, S.; Alimov, Sh., On a time-optimal control problem associated with the heat exchange process, Applied Mathematics & Optimization, 57, 1, 58-68, (2008) · Zbl 1139.49004
[13] Mikhlin, S. G., Linear Partial Differential Equations, (1977), Moscow, Russia: Vysshaya Shkola, Moscow, Russia
[14] Avdonin, S. A.; Ivanov, S. A., Controllability of Systems with Distributed Parameters and Families of Exponents, (1989), Kiev, Ukraine: UMKVO, Kiev, Ukraine
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.