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 the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498
2.
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
3.
A. K. Gushchin, “On the Dirichlet problem for a second-order elliptic equation”, Math. USSR-Sb., 65:1 (1990), 19–66
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
A. K. Gushchin, “Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation”, Sb. Math., 206:10 (2015), 1410–1439
11.
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
12.
A. K. Gushchin, “On the interior smoothness of solutions to second-order elliptic equations”, Siberian Math. J., 46:5 (2005), 826–840
13.
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
14.
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
15.
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
16.
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
17.
A. K. Gushchin, “$L_p$-estimates for solutions of second-order elliptic equation Dirichlet problem”, Theoret. and Math. Phys., 174:2 (2013), 209–219
18.
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
19.
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
20.
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
21.
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
22.
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
23.
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
24.
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
25.
A. K. Gushchin, “Estimates of the nontangential maximal function for solutions of a second-order elliptic equation”, Dokl. Math., 86:2 (2012), 667–669
26.
A. K. Gushchin, “On an estimate of the Dirichlet integral in unbounded domains”, Math. USSR-Sb., 28:2 (1976), 249–261
27.
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
28.
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
29.
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. 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
32.
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
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
34.
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
35.
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
36.
A. K. Guschin, “O vnutrennei gladkosti reshenii ellipticheskogo uravneniya vtorogo poryadka”, Dokl. RAN, 404:1 (2005), 14–17
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, “The rate of stabilization of the solution of a parabolic equation in an unbounded domain”, Differencial'nye Uravnenija, 6 (1970), 741–761
41.
A. K. Gushchin, “Extensions of the space of continuous functions and embedding theorems”, Sb. Math., 211:11 (2020), 1551–1567
42.
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
43.
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
44.
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
A. K. Gushchin, “On the Dirichlet problem for a second order elliptic equation”, Soviet Math. Dokl., 38:2 (1989), 372–376
47.
A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371
48.
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. 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
51.
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. 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. 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. Gushchin, V. P. Mikhajlov, “On stabilization of the solution of the Cauchy problem for a parabolic equation”, Sov. Math. Dokl., 11 (1970), 1215–1219
57.
A. K. Gushchin, “On some properties of elliptic partial differential equation solutions”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2243002 , 9 pp. ;
58.
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
59.
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
60.
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
61.
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
62.
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
63.
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.
64.
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
65.
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
66.
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
67.
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
68.
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
69.
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
70.
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
71.
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
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, “Estimates from below for the solutions of boundary value problems for a parabolic equation”, Dokl. AN SSSR, 203 (1972), 274–277
74.
A. K. Gushchin, “On Dirichlet problem”, Theoret. and Math. Phys., 218:1 (2024), 51–67
75.
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
76.
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
77.
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
78.
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
79.
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
80.
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
81.
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
82.
A. K. Gushchin, Yu. N. Drozhzhinov, V. M. Millionshchikov, V. P. Mikhailov, Differ. Uravn., 25:8 (1989), 1465
83.
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
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
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