nonlinear PDEs of elliptic and parabolic type, stabilization of solutions, Sobolev-Orlicz spaces, degenerate equations, p-Laplacian, Emden-Fowler type equations, asymptotics, conservation laws
Main publications:
M.D. Surnachev, “Stabilization of Solutions to the Dirichlet Problem in a Cylindrical Domain for the Parabolic p-Laplacian”, Journal of Mathematical Sciences, 219:2 (2016), 275-299
M.D. Surnachev, “Holder continuity of solutions to nonlinear parabolic equations degenerated on a part of the domain”, Journal of Mathematical Sciences, 213:4 (2016), 610-635
M.D. Surnachev, V.V. Zhikov, “On density of smooth functions in weighted sobolev spaces with variable exponents”, St Petersburg Mathematical Journal, 27:3 (2016), 415-436
M.D. Surnachev, “A Harnack inequality for weighted degenerate parabolic equations”, Journal of Differential Equations, 248:8 (2010), 2092-2129
M.D. Surnachev, “Estimates for Emden-Fowler type inequalities with absorption term”, Journal of Mathematical Analysis and Applications, 348:2 (2008), 996-1011
P. A. Bakhvalov, M. D. Surnachev, “On stability and accuracy of finite-volume schemes on non-uniform meshes”, Keldysh Institute preprints, 2024, 004, 39 pp.
2022
2.
M. D. Surnachev, “Harnack's Inequality of Weak Type for the Parabolic $p (x)$-Laplacian”, Mat. Zametki, 111:1 (2022), 149–153; Math. Notes, 111:1 (2022), 161–165
3.
M. D. Surnachev, “Estimates of solutions to the noncoercive Dirichlet problem for a second order elliptic equation in divergence form with drift from a Kato class”, Zap. Nauchn. Sem. POMI, 519 (2022), 229–263
2021
4.
P. A. Bakhvalov, M. D. Surnachev, “On analytical families of matrices generating bounded semigroups”, Sib. Zh. Vychisl. Mat., 24:1 (2021), 3–16; Num. Anal. Appl., 14:1 (2021), 1–12
Yu. A. Alkhutov, M. D. Surnachev, “Interior and boundary continuity of $p(x)$-harmonic functions”, Zap. Nauchn. Sem. POMI, 508 (2021), 7–38
2020
6.
Yu. A. Alkhutov, M. D. Surnachev, “Hölder Continuity and Harnack's Inequality for $p(x)$-Harmonic Functions”, Trudy Mat. Inst. Steklova, 308 (2020), 7–27; Proc. Steklov Inst. Math., 308 (2020), 1–21
Yu. A. Alkhutov, M. D. Surnachev, “Estimates of the fundamental solution for an elliptic equation in divergence form with drift”, Zap. Nauchn. Sem. POMI, 489 (2020), 7–35
Yu. A. Alkhutov, M. D. Surnachev, “Harnack inequality for the elliptic $p(x)$-Laplacian with a three-phase exponent $p(x)$”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1329–1338; Comput. Math. Math. Phys., 60:8 (2020), 1284–1293
2019
9.
Yu. A. Alkhutov, M. D. Surnachev, “Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point”, Algebra i Analiz, 31:2 (2019), 88–117; St. Petersburg Math. J., 31:2 (2019), 251–271
P. A. Bakhvalov, M. D. Surnachev, “Linear schemes with several degrees of freedom for the multidimensional transport equation”, Keldysh Institute preprints, 2019, 074, 44 pp.
P. A. Bakhvalov, M. D. Surnachev, “Linear schemes with several degrees of freedom for the 1D transport equation”, Keldysh Institute preprints, 2019, 073, 40 pp.
P. A. Bakhvalov, M. D. Surnachev, “On spectral analysis of numerical schemes for the linear transport equation”, Keldysh Institute preprints, 2019, 070, 28 pp.
Yu. A. Alkhutov, M. D. Surnachev, “Harnack's inequality for the $p(x)$-Laplacian with a two-phase exponent $p(x)$”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 8–56; J. Math. Sci. (N. Y.), 244:2 (2020), 116–147
V. V. Zhikov, M. D. Surnachev, “О плотности гладких функций в весовых соболевских пространствах с переменным показателем”, Algebra i Analiz, 27:3 (2015), 95–124; St. Petersburg Math. J., 27:3 (2016), 415–436
M. D. Surnachev, “On uniqueness of solutions to the problem of stationary diffusion in an incompressible turbulent flow”, Keldysh Institute preprints, 2015, 096, 32 pp.
2014
18.
M. D. Surnachëv, “Regularity of solutions of parabolic equations with a double nonlinearity and a weight”, Tr. Mosk. Mat. Obs., 75:2 (2014), 309–334; Trans. Moscow Math. Soc., 75 (2014), 259–280
M. D. Surnachev, “Asymptotic behavior at infinity for solutions of Emden-Fowler type equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2009, no. 2, 53–56
2019
21.
Yu. A. Alkhutov, V. F. Butuzov, V. V. Kozlov, A. A. Kon'kov, A. V. Mikhalev, E. I. Moiseev, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, I. N. Sergeev, M. D. Surnachev, R. N. Tikhomirov, V. N. Chubarikov, T. A. Shaposhnikova, A. A. Shkalikov, “Vasilii Vasilievich Zhikov”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 5–7; J. Math. Sci. (N. Y.), 244:2 (2020), 113–115
On regularity of p(x)-harmonic functions Yu. A. Alkhutov, M. D. Surnachev Mathematical Colloquium of the Bauman Moscow State Technical University November 25, 2021 17:30
О задаче Коши для параболического $p$-лапласиана M. D. Surnachev Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics November 23, 2011 16:00
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