equations of mathematical physics,
elliptic problems,
free boundary problems.
Main publications:
Demidov A. S., “Asimptotika resheniya kraevoi zadachi dlya ellipticheskikh psevdodifferentsialnykh uravnenii s malym parametrom pri starshem operatore”, Trudy Mosk. matem. ob-va, 32, 1975, 119–146
Demidov A. S., “Some Applications of the Helmholtz–Kirchhoff Method (Equilibrium Plasma in Tokamaks, Hele-Shaw Flow, and High-Frequency Asymptotics)”, Russian J. Math. Phys., 7:2 (2000), 166–186
Demidov A. S., “Ob obratnoi zadache dlya uravneniya Greda–Shafranova s affinnoi pravoi chastyu”, UMN, 55:6 (2000), 131–132
Demidov A. S., Generalized Functions in Mathematical Physics: Main Ideas and Concepts, Nova Science Publishers, Inc., New York, 2001
A. S. Demidov, A. S. Samokhin, “Explicit numerically implementable formulas for Poincaré–Steklov operators”, Zh. Vychisl. Mat. Mat. Fiz., 64:2 (2024), 253–262; Comput. Math. Math. Phys., 64:2 (2024), 237–247
2023
2.
A. S. Demidov, “On explicit numerically realizable formulae for Poincaré–Steklov operators”, Uspekhi Mat. Nauk, 78:6(474) (2023), 181–182; Russian Math. Surveys, 78:6 (2023), 1158–1160
3.
A. S. Demidov, A. S. Kochurov, “Calculation of $n$th derivative with minimum error based on function’s measurement”, Zh. Vychisl. Mat. Mat. Fiz., 63:9 (2023), 1428–1437; Comput. Math. Math. Phys., 63:9 (2023), 1571–1579
2021
4.
A. H. Reda, A. S. Demidov, “Effective data transmission algorithms for distance learning”, Comp. nanotechnol., 8:4 (2021), 19–27
5.
A. S. Demidov, I. V. Demidova, “On the permissible intensity of laser radiation in the optical system and on the technology for measuring the absorption coefficient of its power”, Computer Research and Modeling, 13:5 (2021), 1025–1044
6.
A. S. Demidov, “On Numerically Implementable Explicit Formulas for the Solutions to the 2D and 3D Equations $\operatorname{div}(\alpha(w)\nabla w)=0$ and $\operatorname{div}(\beta\nabla w)=0$ with Cauchy Data on an Analytic Boundary”, Funktsional. Anal. i Prilozhen., 55:1 (2021), 65–72; Funct. Anal. Appl., 55:1 (2021), 52–58
A. S. Demidov, “The inverse problem of magneto-electroencephalography is well-posed: it has a unique solution that is stable with respect to perturbations”, Fundam. Prikl. Mat., 21:4 (2016), 17–22; J. Math. Sci., 245:2 (2020), 1211–124
A. S. Demidov, D. A. Platuschikhin, “Explicit Formula for the Gradient of a Harmonic Function from Its Analytic Cauchy Data on the Analytic Curve”, Mat. Zametki, 87:1 (2010), 141–143; Math. Notes, 87:1 (2010), 135–137
A. S. Demidov, “Reduction of a Nonstationary Euler Hydrodynamic Equation to a System of Ordinary Differential Equations in the Plane Problem of Cavitational Flow with Boundary Control”, Mat. Zametki, 86:1 (2009), 37–50; Math. Notes, 86:1 (2009), 41–52
A. S. Demidov, A. S. Kochurov, A. Yu. Popov, “To the problem of the recovery of nonlinearities in equations of mathematical physics”, Tr. Semim. im. I. G. Petrovskogo, 27 (2009), 74–123; J. Math. Sci. (N. Y.), 163:1 (2009), 46–77
A. S. Demidov, “Helmholtz–Kirchhoff method and boundary control of a plane flow”, Fundam. Prikl. Mat., 12:4 (2006), 65–77; J. Math. Sci., 150:5 (2008), 2335–2343
2005
13.
A. S. Demidov, J. Mwambakana, I. A. Fedotov, “Schwartz Alternating Method for Elliptic Boundary-Value Problems Satisfying the Maximum Principle”, Mat. Zametki, 78:4 (2005), 622–624; Math. Notes, 78:4 (2005), 577–580
A. S. Demidov, “On the evolution of a weak perturbation of a circle in the problem of a Hele–Shaw flow”, Uspekhi Mat. Nauk, 57:6(348) (2002), 177–178; Russian Math. Surveys, 57:6 (2002), 1212–1214
A. S. Demidov, “On the inverse problem for the Grad–Shafranov equation with affine right-hand side”, Uspekhi Mat. Nauk, 56:3(339) (2001), 161–162
2000
16.
A. S. Demidov, “On the inverse problem for the Grad–Shafranov equation with affine right-hand side”, Uspekhi Mat. Nauk, 55:6(336) (2000), 131–132; Russian Math. Surveys, 55:6 (2000), 1141–1142
O. A. Vasilieva, A. S. Demidov, “The finite points model of the Stokes–Leibenson problem for the Hele-Shaw flow”, Fundam. Prikl. Mat., 5:1 (1999), 67–84
A. D. Valiev, A. S. Demidov, “Nonnegative trigonometric polynomials with fixed mean passing through given points”, Mat. Zametki, 62:3 (1997), 468–471; Math. Notes, 62:3 (1997), 390–392
A. S. Demidov, “Complete asymptotics of the solution of the Dirichlet problem for
the two-dimensional Laplace equation with rapidly oscillating boundary
data”, Dokl. Akad. Nauk, 346:6 (1996), 732–734
A. S. Demidov, V. V. Petrova, “An inverse problem with a free boundary in equilibrium plasma theory”, Differ. Uravn., 30:6 (1994), 1034–1038; Differ. Equ., 30:6 (1994), 958–962
1992
21.
A. S. Demidov, E. S. Yatsenko, “Mathematical experiment on heat and mass transfer in the evaporator zone of heat pipes”, TVT, 30:3 (1992), 566–572; High Temperature, 30:3 (1992), 456–462
1983
22.
A. Badzhadi, A. S. Demidov, “Existence, nonexistence and regularity theorems in a problem with a free boundary”, Mat. Sb. (N.S.), 122(164):1(9) (1983), 64–81; Math. USSR-Sb., 50:1 (1985), 67–84
A. S. Demidov, “Asymptotic behavior of the solution of a boundary value problem for elliptic pseudodifferential equations with a small parameter multiplying the highest operator”, Tr. Mosk. Mat. Obs., 32 (1975), 119–146
A. S. Demidov, “Elliptic pseudodifferential boundary value problems with a small parameter in the coefficient of the leading operator”, Mat. Sb. (N.S.), 91(133):3(7) (1973), 421–444; Math. USSR-Sb., 20:3 (1973), 439–463
A. S. Demidov, “Boundary effects and the asymptotic nature of the degeneration of certain elliptic pseudodifferential operators”, Uspekhi Mat. Nauk, 27:1(163) (1972), 245–246
A. S. Demidov, “Asymptotic behavior of the solutions of boundary value problems for a linear second order elliptic equation with coefficients that have a “burst””, Tr. Mosk. Mat. Obs., 23 (1970), 77–112
2021
27.
Yu. A. Nazarova, A. S. Korzin, A. S. Demidov, “Analysis of the prospects for the iot technology in the electric power industry”, Comp. nanotechnol., 8:4 (2021), 9–18
2013
28.
M. S. Agranovich, A. V. Babin, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, S. B. Kuksin, A. P. Kuleshov, V. P. Maslov, S. P. Novikov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirelman, M. A. Shubin, G. I. Eskin, “Marko Iosifovich Vishik (obituary)”, Uspekhi Mat. Nauk, 68:2(410) (2013), 197–200; Russian Math. Surveys, 68:2 (2013), 383–387
2005
29.
V. I. Arnol'd, A. S. Demidov, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, E. F. Mishchenko, K. Yu. Osipenko, A. B. Sossinski, M. A. Tsfasman, V. A. Uspenskii, M. N. Vyalyi, I. V. Yaschenko, M. I. Zelikin, “Vladimir M. Tikhomirov”, Mosc. Math. J., 5:1 (2005), 295
1997
30.
M. S. Agranovich, A. V. Babin, L. R. Volevich, A. Yu. Goritskii, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, M. L. Krasnov, S. B. Kuksin, G. I. Makarenko, V. P. Maslov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirel'man, M. A. Shubin, “Mark Iosifovich Vishik (on his 75th birthday)”, Uspekhi Mat. Nauk, 52:4(316) (1997), 225–232; Russian Math. Surveys, 52:4 (1997), 853–861
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