1966 — graduated from Moscow State University.
1966–1969 — postgraduate in Steklov Mathematical institute.
From 1969 to now — collaborator of the Institute.
1969 — candidate degree. 1974 — doctor degree.
Main publications:
A. K. Guschin, “Stabilizatsiya reshenii vtoroi kraevoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 101(143):4(12) (1976), 459–499; A. K. Gushchin, “Stabilization of the solutions of the second boundary value problem for a second order parabolic equation”, Math. USSR-Sb., 30:4 (1976), 403–440
A. K. Guschin, “O ravnomernoi stabilizatsii reshenii vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 119(161):4(12) (1982), 451–508; A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498
A. K. Guschin, “O zadache Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 137(179):1(9) (1988), 19–64; A. K. Gushchin, “On the Dirichlet problem for a second-order elliptic equation”, Math. USSR-Sb., 65:1 (1990), 19–66
A. K. Guschin, “O vnutrennei gladkosti reshenii ellipticheskikh uravnenii vtorogo poryadka”, Sib. matem. zhurn., 46:5 (2005), 1036–1052; A. K. Gushchin, “On the interior smoothness of solutions to second-order elliptic equations”, Siberian Math. J., 46:5 (2005), 826–840
A. K. Guschin, “Lp-otsenki nekasatelnoi maksimalnoi funktsii dlya resheniya ellipticheskogo uravneniya vtorogo poryadka”, Matem. sb., 207:10 (2016), 28-55
A. K. Gushchin, “On Dirichlet problem”, Theoret. and Math. Phys., 218:1 (2024), 51–67
2022
2.
A. K. Gushchin, “On some properties of elliptic partial differential equation solutions”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2243002 , 9 pp. ;
2020
3.
A. K. Gushchin, “Extensions of the space of continuous functions and embedding theorems”, Sb. Math., 211:11 (2020), 1551–1567
2019
4.
A. K. Gushchin, “On the Existence of $L_2$ Boundary Values of Solutions to an Elliptic Equation”, Proc. Steklov Inst. Math., 306 (2019), 47–65
5.
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
2018
6.
A. K. Gushchin, “The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation”, Sb. Math., 209:6 (2018), 823–839
7.
A. K. Gushchin, “A Criterion for the Existence of $L_p$ Boundary Values of Solutions to an Elliptic Equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64
2016
8.
A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409
2015
9.
A. K. Gushchin, “V.A. Steklov's Work on Equations of Mathematical Physics and Development of His Results in This Field”, Proc. Steklov Inst. Math., 289 (2015), 134–151
10.
A. K. Gushchin, “On the Dirichlet problem for an elliptic equation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 19:1 (2015), 19–43
11.
A. K. Gushchin, “Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation”, Sb. Math., 206:10 (2015), 1410–1439
2013
12.
A. K. Gushchin, “$L_p$-estimates for solutions of second-order elliptic equation Dirichlet problem”, Theoret. and Math. Phys., 174:2 (2013), 209–219
A. K. Gushchin, “The Dirichlet problem for a second-order elliptic equation with an $L_p$ boundary function”, Sb. Math., 203:1 (2012), 1–27
15.
A. K. Gushchin, “Estimates of the nontangential maximal function for solutions of a second-order elliptic equation”, Dokl. Math., 86:2 (2012), 667–669
2011
16.
A. K. Gushchin, “The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a second-order elliptic equation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 53–67
17.
A. K. Gushchin, “Solvability of the Dirichlet problem for a second-order elliptic equation with a boundary function from $L_p$”, Dokl. Math., 83:2 (2011), 219–221
2009
18.
V. S. Vladimirov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zav'yalov, V. A. Il'in, G. I. Marchuk, V. P. Mikhailov, E. I. Moiseev, S. M. Nikol'skii, B. V. Pal'tsev, “Aleksei Alekseevich Dezin (obituary)”, Russian Math. Surveys, 64:3 (2009), 553–560
2008
19.
A. K. Guschin, “Vnutrennie otsenki obobschennykh reshenii ellipticheskogo uravneniya vtorogo poryadka”, Mezhdunarodnaya konferentsiya po matematicheskoi fizike i ee prilozheniyam, Tezisy dokladov (Samara, 8–13 sentyabrya 2008 g.), 2008, 60–63
20.
A. K. Guschin, “Povedenie vblizi granitsy differentsialnykh kharakteristik reshenii elipticheskogo uravneniya vtorogo poryadka”, Vtoroe rossiisko-armyanskoe soveschanie po matematicheskoi fizike, kompleksnomu analizu i smezhnym voprosam, Tezisy dokladov (Moskva, MIAN, 5–11 oktyabrya 2008 g.), 2008, 27–28
21.
A. K. Guschin, V. P. Mikhailov, “O suschestvovanii granichnykh znachenii u reshenii ellipticheskogo uravnenii”, Vestnik SamGU - Estestvennonauchnaya seriya, 2008, no. 8/1(67), 61–75
22.
A. K. Guschin, V. P. Mikhailov, “Vnutrennie otsenki obobschennykh reshenii ellipticheskogo uravneniya vtorogo poryadka”, Vestnik SamGU - Estestvennonauchnaya seriya, 2008, no. 8/1(67), 76–94
23.
A. K. Gushchin, “A strengthening of the interior Hölder continuity property for solutions of the Dirichlet problem for a second-order elliptic equation”, Theoret. and Math. Phys., 157:3 (2008), 1655–1670
2007
24.
A. K. Guschin, “O gladkosti reshenii zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka s kvadratichno summiruemoi granichnoi funktsiei”, Dokl. RAN, 415:1 (2007), 10–13
V. P. Mikhailov, A. K. Gushchin, “Additional chapters of course “Equations of Mathematical Physics””, Lekts. Kursy NOC, 7, Steklov Math. Inst., RAS, Moscow, 2007, 3–144 , 146 pp.
2005
26.
A. K. Guschin, “O vnutrennei gladkosti reshenii ellipticheskogo uravneniya vtorogo poryadka”, Dokl. RAN, 404:1 (2005), 14–17
V. S. Vladimirov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. A. Il'in, G. I. Marchuk, V. P. Mikhailov, E. I. Moiseev, S. M. Nikol'skii, B. V. Pal'tsev, “Aleksei Alekseevich Dezin (on his 80th birthday)”, Russian Math. Surveys, 58:6 (2003), 1237–1240
2002
30.
A. K. Gushchin, “A condition for the compactness of operators in a certain class and its application to the analysis of the solubility of non-local problems for elliptic equations”, Sb. Math., 193:5 (2002), 649–668
2000
31.
A. K. Guschin, “Uslovie polnoi nepreryvnosti operatorov, voznikayuschikh v nelokalnykh zadachakh dlya ellipticheskikh uravnenii”, Dokl. RAN, 373:2 (2000), 161–163
A. K. Gushchin, “Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation”, Sb. Math., 189:7 (1998), 1009–1045
34.
V. S. Vladimirov, A. K. Gushchin, V. A. Il'in, V. N. Maslennikova, V. P. Mikhailov, E. I. Moiseev, B. V. Pal'tsev, V. K. Romanko, A. A. Samarskii, “Alekseǐ Alekseevich Dezin (on the occasion of his 75th birthday)”, Differ. Equ., 34:6 (1998), 721–724
1996
35.
A. K. Guschin, V. P. Mikhailov, “Ob odnoznachnoi razreshimosti nelokalnykh zadach dlya ellipticheskogo uravneniya”, Dokl. RAN, 351:1 (1996), 7–8
A. K. Gushchin, V. P. Mikhailov, “On the continuity of the solutions of a class of non-local problems for an elliptic equation”, Sb. Math., 186:2 (1995), 197–219
37.
A. K. Gushchin, V. P. Mikhailov, “On solvability of nonlocal problems for a second-order elliptic equation”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 101–136
1994
38.
A. K. Gushchin, V. P. Mikhaĭlov, “A condition that a class of nonlocal problems for a second-order elliptic equation be Fredholm”, Russian Acad. Sci. Dokl. Math., 48:3 (1994), 510–514
1993
39.
I. V. Volovich, A. K. Gushchin, A. A. Dezin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zavyalov, V. A. Il'in, V. M. Millionshchikov, V. N. Mikhailov, A. G. Sergeev, “Vladimirov Vasilii Sergeevich (70-th birthday tribute)”, Differential Equations, 29:2 (1993), 305–313
40.
A. A. Logunov, A. A. Slavnov, O. I. Zavialov, O. A. Khrustalev, V. P. Mikhailov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. V. Zharinov, B. I. Zavialov, A. G. Sergeev, V. P. Pavlov, I. Ya. Aref'eva, Yu. A. Tserkovnikov, “The 70th birthday of V. S. Vladimirov”, Theoret. and Math. Phys., 94:1 (1993), 1–2
1992
41.
A. K. Gushchin, V. P. Mikhailov, “On the existence of boundary values of solutions of an elliptic equation”, Math. USSR-Sb., 73:1 (1992), 171–194
1991
42.
V. S. Vladimirov, A. K. Guschin, A. A. Dezin, V. I. Zavyalov, V. M. Millionschikov, “Valentin Petrovich Mikhailov (k shestidesyatiletiyu so dnya rozhdeniya)”, Differents. uravneniya, 27:4 (1991), 725–730
43.
V. S. Vladimirov, A. K. Gushchin, A. A. Dezin, Yu. N. Drozhzhinov, B. I. Zavialov, V. M. Millionshchikov, “Valentin Petrovich Mikhailov (on his sixtieth birthday)”, Russian Math. Surveys, 46:4 (1991), 207–209
1989
44.
A. K. Gushchin, Yu. N. Drozhzhinov, V. M. Millionshchikov, V. P. Mikhailov, Differ. Uravn., 25:8 (1989), 1465
1988
45.
A. K. Guschin, “O zavisimosti povedeniya pri bolshikh znacheniyakh vremeni resheniya parabolicheskogo uravneniya ot dannykh zadachi”, Kachestvennaya teoriya differentsialnykh uravnenii (Irkutsk, 1986), ed. V. M. Matrosov, Nauka, Sibirsk. otd., Novosibirsk, 1988, 72–82
1989
46.
A. K. Gushchin, “On the Dirichlet problem for a second order elliptic equation”, Soviet Math. Dokl., 38:2 (1989), 372–376
1990
47.
A. K. Gushchin, “On the Dirichlet problem for a second-order elliptic equation”, Math. USSR-Sb., 65:1 (1990), 19–66
1989
48.
A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371
1986
49.
A. K. Guschin, V. P. Mikhailov, “O ravnomernoi kvaziasimptotike resheniya zadachi Koshi dlya giperbolicheskogo uravneniya”, Dokl. AN SSSR, 287:1 (1986), 37–40
A. K. Gushchin, V. P. Mikhailov, “On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation”, Math. USSR-Sb., 59:2 (1988), 409–427
51.
O. I. Bogoyavlenskii, V. S. Vladimirov, I. V. Volovich, A. K. Gushchin, Yu. N. Drozhzhinov, V. V. Zharinov, V. P. Mikhailov, “Boundary value problems of mathematical physics”, Proc. Steklov Inst. Math., 175 (1988), 65–105
1986
52.
A. K. Gushchin, V. P. Mikhailov, “Uniform quasi-asymptotic behavior of the solution of the Cauchy problem for a hyperbolic equation”, Dokl. Akad. Nauk SSSR, 287:1 (1986), 37–40
1985
53.
A. K. Guschin, V. P. Mikhailov, Yu. A. Mikhailov, “Otsenki funktsii Grina i kriterii ravnomernoi stabilizatsii resheniya vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Dokl. AN SSSR, 282:1 (1985), 15–18
A. K. Gushchin, V. P. Mikhailov, Yu. A. Mikhailov, “On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation”, Math. USSR-Sb., 56:1 (1987), 141–162
1985
55.
A. K. Gushchin, V. P. Mikhailov, Yu. A. Mikhailov, “Estimates for the Green function and a criterion for uniform stabilization of the solution of the second mixed problem for a second-order parabolic equation”, Dokl. Akad. Nauk SSSR, 282:1 (1985), 15–18
1984
56.
A. K. Guschin, V. P. Mikhailov, “O ravnomernoi kvazistabilizatsii resheniya zadachi Koshi dlya giperbolicheskogo uravneniya”, Dokl. AN SSSR, 276:3 (1984), 532–535
A. K. Gushchin, V. P. Mikhailov, “Uniform stabilization of the solution of the Cauchy problem for a second-order hyperbolic equation”, Proc. Steklov Inst. Math., 166 (1986), 79–95
1984
58.
A. K. Gushchin, V. P. Mikhailov, “Uniform quasistabilization of the solution of the Cauchy problem for a hyperbolic equation”, Dokl. Akad. Nauk SSSR, 276:3 (1984), 532–535
1982
59.
A. K. Guschin, “A criterion for uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Dokl. AN SSSR, 264:5 (1982), 1041–1045
A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498
1981
61.
V. S. Vladimirov, A. K. Guschin, A. A. Dezin, V. M. Millionschikov, L. S. Pontryagin, “Valentin Petrovich Mikhailov (k pyatidesyatiletiyu so dnya rozhdeniya)”, Differents. uravneniya, 17:4 (1981), 757–762
1980
62.
A. K. Guščin, “On the behaviour as $t\rightarrow \infty $ of solutions of the second mixed problem for a second-order parabolic equation”, Appl. Math. Optim., 6:2 (1980), 169–180
63.
A. K. Gushchin, V. P. Mikhailov, “On boundary values in $L_p$, $p>1$, of solutions of elliptic equations”, Math. USSR-Sb., 36:1 (1980), 1–19
1978
64.
A. K. Guschin, V. P. Mikhailov, “O povedenii vblizi granitsy resheniya tretei kraevoi zadachi dlya ellipticheskogo uravneniya vtorogo poryadka”, Kompleksnyi analiz i ego prilozheniya, Nauka, M., 1978, 193–202
1976
65.
A. K. Guschin, V. P. Mikhailov, “The behavior in the neighborhood of the boundary of a solution of the third boundary value problem for an elliptic equation”, Dokl. AN SSSR, 229:6 (1976), 1299–1302
66.
A. K. Guschin, “O povedenii pri $t\to\infty$ reshenii vtoroi kraevoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Dokl. AN SSSR, 227:2 (1976), 273–276
A. K. Gushchin, “Stabilization of the solutions of the second boundary value problem for a second order parabolic equation”, Math. USSR-Sb., 30:4 (1976), 403–440
68.
A. K. Gushchin, “On an estimate of the Dirichlet integral in unbounded domains”, Math. USSR-Sb., 28:2 (1976), 249–261
1975
69.
A. K. Guschin, V. P. Mikhailov, A. L. Muravei, “O stabilizatsii reshenii nestatsionarnykh granichnykh zadach dlya lineinykh uravnenii v chastnykh proizvodnykh”, Nekotorye problemy gazovoi dinamiki, Dinamika sploshnoi sredy, 23, 1975, 57–91
70.
A. K. Gushchin, “Some properties of a generalized solution of the second boundary-value problem for a parabolic equation”, Math. USSR-Sb., 26:2 (1975), 225–244
1973
71.
A. K. Gushchin, “The estimates of the solutions of boundary value problems for a second order parabolic equation”, Proc. Steklov Inst. Math., 126 (1973), 1–46
1972
72.
A. K. Guschin, V. P. Mikhailov, “O povedenii pri $t\to\infty$ resheniya zadachi Koshi dlya parabolicheskogo uravneniya”, Primenenie funktsionalnykh metodov k kraevym zadacham matematicheskoi fiziki, Materialy III-go Sovetsko-chekhoslovatskogo soveschaniya, In-t matematiki AN SSSR, Sibirskoe otd., Novosibirsk, 1972, 45–49
73.
A. K. Guschin, “Ob otsenkakh reshenii II i III kraevykh zadach dlya parabolicheskogo uravneniya vtorogo poryadka v neogranichennykh po prostranstvennym peremennym oblastyakh”, Dokl. AN SSSR, 206 (1972), 788–791
A. K. Guschin, “Estimates from below for the solutions of boundary value problems for a parabolic equation”, Dokl. AN SSSR, 203 (1972), 274–277
1971
76.
A. K. Gushchin, V. P. Mikhailov, “The stabilization of the solution of the Cauchy problem for a parabolic equation with one space variable”, Proc. Steklov Inst. Math., 112 (1971), 187–210
77.
A. K. Guščin, V. P. Mihaĭlov, “The stabilization of the solution of the Cauchy problem for a parabolic equation”, Differencial'nye Uravnenija, 7:2 (1971), 297–311
78.
A. K. Gushchin, V. P. Mikhajlov, “On stabilization of the solution of the Cauchy problem for a one-dimensional parabolic equation”, Sov. Math. Dokl., 12 (1971), 419–422
1970
79.
A. K. Gushchin, V. P. Mikhajlov, “On stabilization of the solution of the Cauchy problem for a parabolic equation”, Sov. Math. Dokl., 11 (1970), 1215–1219
80.
A. K. Gushchin, “The rate of stabilization of the solution of a parabolic equation in an unbounded domain”, Differencial'nye Uravnenija, 6 (1970), 741–761
1969
81.
A. K. Gushchin, “On the speed of stabilization of the solutions of a boundary problem for a parabolic equation”, Siberian Math. J., 10:1 (1969), 30–40
1968
82.
A. K. Guschin, “O stabilizatsii resheniya parabolicheskogo sravneniya”, Kraevye zadachi dlya differentsialnykh uravnenii. II, Tr. MIAN SSSR, 103, 1968, 51–57
A. K. Gushchin, “Some estimates of solutions of boundary value problems for an equation of heat conduction in an unbounded domain”, Proc. Steklov Inst. Math., 91 (1967), 1–16
On the Dirichlet problem A. K. Gushchin International Conference Dedicated to the 100th Anniversary of the Birthday
of V. S. Vladimirov (Vladimirov-100) January 9, 2023 16:00
Some properties of solutions of elliptic equations A. K. Gushchin International Conference "Selected Topics in Mathematical Physics" Dedicated to 75-th Anniversary of I. V. Volovich September 30, 2021 16:40
V. P. Mikhailov, A. K. Gushchin, Additional chapters of course “Equations of Mathematical Physics”, Lekts. Kursy NOC, 7, 2007, 146 с. http://mi.mathnet.ru/book649
2024
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