01.01.05 (Probability theory and mathematical statistics)
E-mail:
,
Keywords:
Wave and Klein–Gordon equations,
harmonic crystals,
coupled Hamilton systems,
Cauchy problem,
random initial data,
weak convergence of measures,
space-time scaling,
hydrodynamic limit,
energy transport equation.
Scattering theory. Ergodicity and mixing of random processes. Long-time behavior of solutions for partial differential equations of the hyperbolic type, for the difference equations and for coupled systems, with random initial data. Weak convergence of measures. The derivation of hydrodynamic equations.
Biography
1985–1990 — Graduate course of Department of Mechanics and Mathematics, Lomonosov Moscow State University
1990 — M.Sc. degree with Honour in Mathematics from Lomonosov Moscow State University. Graduation thesis "Connection between the scattering matrix and scattering amplitude for symmetric hyperbolic systems" (supervisor Prof. B.R. Vainberg).
1990–1993 — post-graduate course of chair "Differential Equations", Department of Mechanics and Mathematics, Lomonosov Moscow State University.
1994 — Ph.D. degree in Differential Equations from Lomonosov Moscow State University.
Ph.D. thesis "Ergodic properties of hyperbolic equations with mixing" (supervisor Prof. A.I.Komech).
2002–2005 — Doctor's course at Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (scientific adviser Prof. L.R. Volevich).
2007 — Doctor's degree in Probability Theory from Saint-Petersburg Branch of Steklov Mathematical Institute of Russian Academy of Sciences. Thesis for a Doctor's degree: "On convergence to equilibrium for statistical solutions of the partial differential equations and difference equations. Two-temperature problem with mixing".
Main publications:
T.V. Dudnikova, H. Spohn, “Local stationary for lattice dynamics in the harmonic approximation”, Markov Processes and Related Fields, 12:4 (2006), 645-678 , arXiv: math-ph/0505031
T. V. Dudnikova, A. I. Komech, “On a two-temperature problem for Klein–Gordon equation”, Theory Probab. Appl., 50:4 (2006), 582–611
T.V. Dudnikova, A.I. Komech, N. Mauser, “On the convergence to a statistical equilibrium in the crystal coupled to a scalar field”, Russian Journal of Mathematical Physics, 12:3 (2005), 301-325 , arXiv: math-ph/0508053
T.V. Dudnikova, A.I. Komech, N. Mauser, “On two-temperature problem for harmonic crystals”, Journal of Statistical Physics, 114:3/4 (2004), 1035-1083 , arXiv: math-ph/0211017
T.V. Dudnikova, A.I. Komech, H. Spohn, “On a two-temperature problem for wave equation”, Markov Processes and Related Fields, 8:1 (2002), 43-80 , arXiv: math-ph/0508044
T. V. Dudnikova, “Deriving hydrodynamic equations for a Hamiltonian “field-lattice” system”, Dokl. RAN. Math. Inf. Proc. Upr., 521 (2025), 32–37; Dokl. Math., 111:1 (2025), 20–24
2.
T. V. Dudnikova, “Stabilization of space–time statistical solutions for Dirac equations”, Mat. Zametki, 118:6 (2025), 957–962
2024
3.
T. V. Dudnikova, “Stabilization of the statistical solutions for large times for a harmonic lattice coupled to a Klein–Gordon field”, TMF, 218:2 (2024), 280–305; Theoret. and Math. Phys., 218:2 (2024), 241–263
T. V. Dudnikova, “On the stationary non-equilibrium measures for the “field–crystal” system”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 37–40; Dokl. Math., 106:2 (2022), 332–335
T. V. Dudnikova, “Convergence to stationary non-equilibrium states for Klein–Gordon equations”, Izv. RAN. Ser. Mat., 85:5 (2021), 110–131; Izv. Math., 85:5 (2021), 932–952
T. V. Dudnikova, “On stationary nonequilibrium measures for wave equations”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 27–30; Dokl. Math., 101:3 (2020), 195–197
8.
T. V. Dudnikova, “Space-time statistical solutions for the Hamiltonian field-crystal system”, Keldysh Institute preprints, 2020, 089, 20 pp.
9.
T. V. Dudnikova, “Stabilization of Statistical Solutions for an Infinite Inhomogeneous Chain of Harmonic Oscillators”, Trudy Mat. Inst. Steklova, 308 (2020), 181–196; Proc. Steklov Inst. Math., 308 (2020), 168–183
T. V. Dudnikova, “The limiting amplitude principle for the nonlinear Lamb system”, Probl. Anal. Issues Anal., 8(26):3 (2019), 45–62
2018
11.
T. V. Dudnikova, “Infinite non homogeneous chain of harmonic oscillators: Stabilization of statistical solutions”, Keldysh Institute preprints, 2018, 254, 24 pp.
12.
T. V. Dudnikova, “The asymptotic behavior of solutions to the Cauchy problem with periodic initial data for the nonlinear Lamb system”, Keldysh Institute preprints, 2018, 206, 16 pp.
13.
T. V. Dudnikova, “On the non-equilibrium states of the crystal lattice”, Keldysh Institute preprints, 2018, 015, 26 pp.
T. V. Dudnikova, “Virial identities and energy-momentum relation for solitary waves of nonlinear Dirac equations”, Keldysh Institute preprints, 2018, 012, 36 pp.
15.
T. V. Dudnikova, “Large-time behavior of an infinite system of harmonic oscillators on the half-line”, Trudy Mat. Inst. Steklova, 301 (2018), 91–107; Proc. Steklov Inst. Math., 301 (2018), 82–97
T. V. Dudnikova, “Infinite non homogeneous chain of harmonic oscillators: Large-time behavior of solutions”, Keldysh Institute preprints, 2017, 109, 35 pp.
T. V. Dudnikova, “On the Asymptotic Normality of a Harmonic Crystal Coupled to a Wave Field”, Mat. Zametki, 99:6 (2016), 941–944; Math. Notes, 99:6 (2016), 942–945
2011
19.
T. V. Dudnikova, “Deriving hydrodynamic equations for lattice systems”, TMF, 169:3 (2011), 352–367; Theoret. and Math. Phys., 169:3 (2011), 1668–1682
T. V. Dudnikova, “Convergence to equilibrium of the wave equation in $\mathbb R^n$ with odd $n\geqslant3$”, Uspekhi Mat. Nauk, 61:1(367) (2006), 177–178; Russian Math. Surveys, 61:1 (2006), 168–170
2005
21.
T. V. Dudnikova, “Stabilization of statistical solutions to the wave equation in the even-dimensional space”, Keldysh Institute preprints, 2005, 080, 36 pp.
T. V. Dudnikova, “On convergence to equilibrium for wave equations in $\mathbb R^n$, with odd $n\ge3$”, Keldysh Institute preprints, 2005, 077, 32 pp.
23.
T. V. Dudnikova, A. I. Komech, “On a two-temperature problem for Klein–Gordon equation”, Teor. Veroyatnost. i Primenen., 50:4 (2005), 675–710; Theory Probab. Appl., 50:4 (2006), 582–611
T. V. Dudnikova, A. I. Komech, “Ergodic properties of hyperbolic equations with mixing”, Teor. Veroyatnost. i Primenen., 41:3 (1996), 505–519; Theory Probab. Appl., 41:3 (1997), 436–448
T. V. Dudnikova, “A connection between the scattering matrix and the scattering amplitude for symmetric hyperbolic systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 4, 3–6
26.
T. V. Dudnikova, “Ergodicity of the phase flow of the wave equation with mixing”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 1, 17–22
