Geodesic
Inverse problem for Sobolev type mathematical models
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 2, pp. 25-36

Voir la notice de l'article provenant de la source Math-Net.Ru

The work is devoted to the study of an inverse problem for the linear Sobolev type equation of higher order with an unknown coefficient depending on time. Since the equation might be degenerate the phase space method is used. It consists in construction of projectors splitting initial spaces into a direct sum of subspaces. Actions of operators also split. Therefore, the initial problem is reduced to two problems: regular and singular. The regular one is reduced to the first order nondegenerate problem which is solved via approximations. The needed smoothness of the solution is obtained. Then it is substituted into the singular problem which is solved using the methods of relatively polynomially bounded operator pencils theory. The main result of the work contains sufficient conditions for the existence and uniqueness of the solution to the inverse problem for a complete Sobolev type model of the second order. This technique can be used to investigate inverse problems of the considered type for Boussinesq–Love mathematical model.
Keywords: inverse problem, mathematical models, equation of second order.
Mots-clés : Sobolev type equation 
@article{VYURU_2019_12_2_a1,
     author = {A. A. Zamyshlyaeva and A. V. Lut},
     title = {Inverse problem for {Sobolev} type mathematical models},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {25--36},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a1/}
}
TY  - JOUR
AU  - A. A. Zamyshlyaeva
AU  - A. V. Lut
TI  - Inverse problem for Sobolev type mathematical models
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2019
SP  - 25
EP  - 36
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a1/
LA  - en
ID  - VYURU_2019_12_2_a1
ER  - 
%0 Journal Article
%A A. A. Zamyshlyaeva
%A A. V. Lut
%T Inverse problem for Sobolev type mathematical models
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2019
%P 25-36
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a1/
%G en
%F VYURU_2019_12_2_a1
A. A. Zamyshlyaeva; A. V. Lut. Inverse problem for Sobolev type mathematical models. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 2, pp. 25-36. http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a1/