Gurevich, Pavel Leonidovich

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Total publications: 11
Scientific articles: 11
Presentations: 2

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Doctor of physico-mathematical sciences (2009)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 29.11.1977
E-mail: , , , , ,
Keywords: Boundary Value Problems for Functional Differential Equations; Nonlocal Elliptic Problems.


1) Boundary Value Problems for Differential-Difference Equations: a) Fredholm solvability of a boundary value problem for one class of differential-difference equations is proved in the one-dimensional case; b) Smoothness of generalized solutions (which may violate inside the interval) is investigated. It is proved that smoothness of a generalized solution preserves if one impacts a finite number of orthogonality conditions on the right-hand side. 2) Elliptic problems with nonlocal conditions near a boundary of domain: a) For model problems in plane and dihedral angles (that arise when studying nonlocal problems in bounded domains), the Green formula and adjoint problems are obtained. Necessary and sufficient conditions for one-valued and Fredholm solvability of model problems in the Kondrat'ev weighted spaces are proved (earlier only sufficient conditions were obtained by A. L. Skubachevskii). b) Coefficients in asymptotic (near some special set) formulas of solutions to nonlocal problems are calculated. These coefficients depend on eigenvectors and associate vectors of adjoint problems. c) Fredholm solvability of nonlocal elliptic problems in bounded domains is proved for the case of nonlinear (near some special set) argument transformations. It is shown that index of a problem with nonlinear argument transformations is equal to index of the corresponding problem with linear argument transformation. d) Fredholm solvability of elliptic equations with nonlocal conditions near a boundary is proved in the Sobolev spaces (with no weight). Asymptotics of solutions to nonlocal problem is considered in the Sobolev spaces. e) Smoothness of solutions to 2nd order elliptic equations with nonlocal conditions is studied in the Sobolev spaces.



February 2000, graduated (with honors) Moscow State Aviation Institute (technical university), Master in Applied Mathematics, specialty — Differential Equations.

2000 — up to now, Post-graduate student of the Department of Differential Equations in MAI.

In 1997–1998 — was awarded by the scholarship of Russia Government for students; in 1998–2000 — was awarded by the scholarship of Russia President for students; in 2001–2002 — was awarded by the scholarship of Russia Government for post-graduate students. I participated in the following international conferences: a) International Conference on Differential and Functional-Differential Equations, Moscow, 1999. b) International Conference "Differential Equations and Related Topics" dedicated to the Centenary Anniversary of I. G. Petrovskii, Moscow, 2001.

Main publications:
  • Gurevich P. L. Solvability of the boundary value problem for some differential–difference equations // Functional Differential Equations. 1998, v. 5, no. 1–2, p. 139–157.
  • Gurevich P. L. On fredholm solvability of boundary value problem for differential–difference equations // Abstracts of international conference on differential and functional-differential equations. Moscow, 1999, p. 42–43.
  • Gurevich P. L. Nonlocal problems for elliptic equations in dihedral angles and the Green formula // Mitteilungen aus dem Mathem. Seminar Giessen, Math. Inst. Univ. Giessen, Germany, Heft 247, 2001, p. 1–74.
  • Gurevich P. L. On the Green formula for nonlocal elliptic problems // Abstracts of International Conf. "Differential Equations and Related Topics" dedicated to the Centenary Anniversary of I. G. Petrovskii, Moscow, MSU, 2001. P. 159–160.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. P. Gurevich, “Asymptotics of parabolic Green's functions on lattices”, Algebra i Analiz, 28:5 (2016),  21–60  mathnet  mathscinet  elib; St. Petersburg Math. J., 28:5 (2017), 569–596  isi  scopus
2. Pavel Gurevich, Dmitrii Rachinskii, “Well-posedness of parabolic equations containing hysteresis with diffusive thresholds”, Trudy MIAN, 283 (2013),  92–114  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 283 (2013), 87–109  isi
3. P. L. Gurevich, “Elliptic problems with nonlocal boundary conditions and Feller semigroups”, CMFD, 38 (2010),  3–173  mathnet  mathscinet  zmath; Journal of Mathematical Sciences, 182:3 (2012), 255–440  scopus
4. P. L. Gurevich, “Bounded Perturbations of Two-Dimensional Diffusion Processes with Nonlocal Conditions near the Boundary”, Mat. Zametki, 83:2 (2008),  181–198  mathnet  mathscinet  zmath  elib; Math. Notes, 83:2 (2008), 162–179  isi  elib  scopus
5. P. L. Gurevich, “On the non-existence of Feller semigroups in the non-transversal case”, Uspekhi Mat. Nauk, 63:3(381) (2008),  159–160  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:3 (2008), 565–566  isi  elib  scopus
6. P. L. Gurevich, “On the Existence of a Feller Semigroup with Atomic Measure in a Nonlocal Boundary Condition”, Trudy MIAN, 260 (2008),  164–179  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 260 (2008), 157–171  isi  elib  scopus
7. P. L. Gurevich, “On the index instability for some nonlocal elliptic problems”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007),  179–194  mathnet  mathscinet  elib; J. Math. Sci. (N. Y.), 143:4 (2007), 3293–3302  scopus
8. P. L. Gurevich, “On the Stability of the Index of Unbounded Nonlocal Operators in Sobolev Spaces”, Trudy MIAN, 255 (2006),  116–135  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 255 (2006), 108–126  scopus
9. P. L. Gurevich, “Generalized Solutions of Nonlocal Elliptic Problems”, Mat. Zametki, 77:5 (2005),  665–682  mathnet  mathscinet  zmath  elib; Math. Notes, 77:5 (2005), 614–629  isi  elib  scopus
10. P. L. Gurevich, “Non-local elliptic problems with non-linear argument transformations near the points of conjugation”, Izv. RAN. Ser. Mat., 67:6 (2003),  71–110  mathnet  mathscinet  zmath; Izv. Math., 67:6 (2003), 1149–1186  isi  scopus
11. P. L. Gurevich, “Solvability of Nonlocal Elliptic Problems in Dihedral Angles”, Mat. Zametki, 72:2 (2002),  178–197  mathnet  mathscinet  zmath; Math. Notes, 72:2 (2002), 158–176  isi  scopus

Presentations in Math-Net.Ru
1. Уравнения реакции-диффузии с гистерезисом
P. L. Gurevich
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
March 21, 2012 16:00
2. О периодических решениях задачи термоконтроля с гистерезисом
P. L. Gurevich
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
March 31, 2010 16:00

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