Abstract:
Sufficient solvability conditions of the start control and final observation problem in a weak gener- alized meaning for one abstract quasilinear Sobolev type equation are obtained. Sobolev type equations constitute a large area of nonclassical equations of mathematical physics. Techniques used in this article originated in the theory of semilinear Sobolev type equations. Solvability of the start control and final observation problem for the Barenblatt–Gilman model describing the nonequilibrium countercurrent capillary impregnation was proved on the basis of abstract results. The unknown function corresponds to effective saturation. The main equation of this model is nonlinear and implicit with respect to the time derivative which makes it quite difficult to study. Formulation of this problem agrees with consideration of the effect of disequilibrium, which is the characteristic feature of the considered model.
Keywords:
quasi-linear Sobolev type equations; start control and final observation problem; weak generalized solution; Barenblatt–Gilman model.
Received: 29.07.2015
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: Russian
Citation:
E. A. Bogatyreva, “The start control and final observation problem for a quasi-linear Sobolev type equation”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 5–10
\Bibitem{Bog15}
\by E.~A.~Bogatyreva
\paper The start control and final observation problem for a quasi-linear Sobolev type equation
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2015
\vol 7
\issue 4
\pages 5--10
\mathnet{http://mi.mathnet.ru/vyurm271}
\crossref{https://doi.org/10.14529/mmph150401}
\elib{https://elibrary.ru/item.asp?id=24389497}
Linking options:
https://www.mathnet.ru/eng/vyurm271
https://www.mathnet.ru/eng/vyurm/v7/i4/p5
This publication is cited in the following 6 articles:
K. V. Perevozchikova, N. A. Manakova, “Investigation of boundary control and final observation in mathematical model of motion speed potentials distribution of filtered liquid free surface”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:2 (2023), 111–116
K. V. Perevozhikova, N. A. Manakova, “Chislennoe modelirovanie startovogo upravleniya i finalnogo nablyudeniya v modeli filtratsii zhidkosti”, J. Comp. Eng. Math., 8:1 (2021), 29–45
K. V. Vasiuchkova, “Chislennoe issledovanie dlya zadachi startovogo upravleniya i finalnogo nablyudeniya v modeli raspredeleniya potentsialov v kristallicheskom poluprovodnike”, J. Comp. Eng. Math., 6:3 (2019), 54–68
N. A. Manakova, K. V. Vasiuchkova, “Numerical investigation for the start control and final observation problem in model of an I-beam deformation”, J. Comp. Eng. Math., 4:2 (2017), 26–40
N. A. Manakova, “On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model”, J. Comp. Eng. Math., 3:4 (2016), 59–72
N. A. Manakova, E. A. Bogatyreva, 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), 2016, 1
Citation in format AMSBIB
Contact us: