optimal boundary control, asymptothic methods for fast oscillation functions, math. methods in economics.
Main publications:
V.V. Grushin, S.Yu. Dobrokhotov, S.A. Sergeev, “Osrednenie i dispersionnye effekty v zadacha o rasprostranenii voln, porozhdennykh lokalizovannym istochnikom.”, Trudy MIAN, 281 (2013), 170-187
S.Yu. Dobrokhotov, S.A. Sergeev, B. Tirozzi., “Asymptotic Solutions of the Cauchy Problem with Localized Initial Conditions for Linearized Two-Dimensional Boussinesq-Type Equations with Variable Coefficients.”, Russian Journal of Mathematical Physics, 20:2 (2013), 155-171
S. A. Sergeev, “Asymptotics of the Head Wave in the Cauchy Problem for a Difference Scheme Corresponding to the Two-Dimensional Wave Equation with Localized Initial Data”, Mat. Zametki, 109:6 (2021), 884–900; Math. Notes, 109:6 (2021), 918–931
2019
2.
S. A. Sergeev, “Asymptotic Solutions of the Cauchy Problem with Localized Initial Data for a Finite-Difference Scheme Corresponding to the One-Dimensional Wave Equation”, Mat. Zametki, 106:5 (2019), 744–760; Math. Notes, 106:5 (2019), 800–813
S. A. Sergeev, “Asymptotic Solutions of One-Dimensional Linear Evolution Equations for Surface Waves with Account for Surface Tension”, Mat. Zametki, 103:3 (2018), 475–480; Math. Notes, 103:3 (2018), 499–504
S. A. Sergeev, A. A. Tolchennikov, “Creation Operators in the Problem of Localized Solutions of the Linearized Shallow Water Equations with Regular and Singular Characteristics”, Mat. Zametki, 100:6 (2016), 911–922; Math. Notes, 100:6 (2016), 852–861
V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”, Trudy Mat. Inst. Steklova, 281 (2013), 170–187; Proc. Steklov Inst. Math., 281 (2013), 161–178
D. A. Lozhnikov, S. A. Sergeev, “On the Behavior of the Localized Solution of the Wave Equation in a Neighborhood of the Localization Point for Small Times”, Mat. Zametki, 91:1 (2012), 149–153; Math. Notes, 91:1 (2012), 141–146
V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Correction to the paper “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source” (Proc. Steklov Inst. Math. 281, 161–178 (2013))”, Trudy Mat. Inst. Steklova, 288 (2015), 287; Proc. Steklov Inst. Math., 288 (2015), 265
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