Formulas in the theory of identification
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1522-1539.

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

The paper is devoted to some identification problems for evolution and other partial differetial equation. Explicit formulas are obtained and discussed.
Keywords: identification problems, the second order partial differential equations.
Mots-clés : evolution equations
@article{SEMR_2020_17_a99,
     author = {Yu. E. Anikonov},
     title = {Formulas in the theory of identification},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1522--1539},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a99/}
}
TY  - JOUR
AU  - Yu. E. Anikonov
TI  - Formulas in the theory of identification
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 1522
EP  - 1539
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a99/
LA  - ru
ID  - SEMR_2020_17_a99
ER  - 
%0 Journal Article
%A Yu. E. Anikonov
%T Formulas in the theory of identification
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 1522-1539
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a99/
%G ru
%F SEMR_2020_17_a99
Yu. E. Anikonov. Formulas in the theory of identification. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1522-1539. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a99/

[1] A.N. Tikhonov, V.Ya. Arsenin, Solutions of Ill-Posed Problems, Winston, Washington, 1977 | MR | Zbl

[2] M.M. Lavrent'ev, V.G. Romanov, S.P. Shishatskij, Ill-Posed Problems of Mathematical Physics and Analysis, American Mathematical Society, Providence, 1986 | MR | Zbl

[3] I. Gelfand, “Some aspects of functional analysis and algebra”, Proc. internat. Congr. Math. (1954 Amsterdam), v. I, Amsterdam, 1957, 253–276 | MR | Zbl

[4] J.W. Forrester, World Dynamics, Wright-Allen Press, Cambridge (Mass.), 1971 | MR

[5] S.A. Makhov, “Mathematical modeling of the world dynamics and sustainable development on the model of Forrester”, New in Synergetics. New reality. New Problems. New Generation, Nauka, M., 2007, 79–101

[6] J. Riordan, An Introduction to Combinatorial Analysis, Princeton University Press, Princeton, 1980 | MR | Zbl

[7] I.V. Kuznetsov, M.V. Rodkin, D.V. Serebryakov, O.B. Uryadov, “Hierarchical approach to dynamics of criminality”, New in Synergetics. New reality. New Problems. New Generation, Nauka, M., 2007, 203–228

[8] G.G. Malinetskii, I.V. Kuznetsov, A.V. Podlazov, “On national system of scientific monitoring”, New in Synergetics. New reality. New Problems. New Generation, Nauka, M., 2007, 40–78

[9] Yu.E. Anikonov, “The identification problem for the functional equation with a parameter”, J. Inverse Ill-Posed Probl., 20:4 (2012), 401–409 | DOI | MR | Zbl

[10] Yu.E. Anikonov, M.V. Neshchadim, “On inverse problems for equations of mathematical physics with parameter”, Sib. Elektron. Mat. Izv., 9 (2012), 45–64 | MR | Zbl

[11] Yu.E. Anikonov, M.V. Neshchadim, “On a method of studying identification problems for the second order equations”, J. Appl. Ind. Math., 13:1 (2019), 11–21 | DOI | MR | Zbl

[12] Yu.E. Anikonov, N.B. Ayupova, “Ray expansions and identities for second order equations. Applications to inverse problems”, J. Math. Sci., 231:2 (2018), 111–123 | DOI | MR | Zbl

[13] P. Lévy, Concrete problems of functional analysis, Gauthier-Villars, Paris, 1951 | MR | Zbl

[14] Yu.E. Anikonov, “Formulas in a problem of the search of the symbol of an linear operator”, Sib. Elektron. Mat. Izv., 8 (2011), 163–167 | MR | Zbl

[15] Yu.E. Anikonov, N.B. Ayupova, V.G. Bardakov, V.P. Golubyatnikov, M.V. Neshchadim, “Inversion of mapping and inverse problems”, Sib. Elektron. Mat. Izv., 9 (2012), 382–432 | MR | Zbl

[16] Yu.E. Anikonov, M.V. Neshchadim, “Representations for the solutions and coefficients of second-order differential equations”, J. Appl. Ind. Math., 7:1 (2013), 15–21 | DOI | MR | Zbl

[17] Yu.E. Anikonov, M.V. Neshchadim, “Representations for the solutions and coefficients of evolution equations”, J. Appl. Ind. Math., 7:3 (2013), 326–334 | DOI | MR | Zbl

[18] N.L. Abasheeva, Yu.E. Anikonov, “Operator formulae in the inverse problems for evolution equations”, J. Math. Sci., 237:4 (2019), 501–510 | DOI | MR | Zbl

[19] Yu.E. Anikonov, N.B. Ayupova, “Remarks on identification theory”, Sib. Elektron. Mat. Izv., 15 (2018), 1091–1102 | MR | Zbl

[20] Yu.E. Anikonov, “Functional equations and identification problems”, Sib. Zh. Chist. Prikl. Mat., 18:2 (2018), 3–12 | DOI | MR | Zbl

[21] Yu.E. Anikonov, M.P. Vishnevskii, “Reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces”, Sib. Math. J., 35:3 (1994), 439–458 | DOI | MR | Zbl

[22] Yu.E. Anikonov, “Analytical representations of solutions to multidimensional inverse problems for evolutionary equations”, Dokl. Math., 54:3 (1996), 838–841 | MR | Zbl