Muravnik, Andrey Borisovich

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Total publications: 16
Scientific articles: 16
Presentations: 2

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Doctor of physico-mathematical sciences (2011)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Keywords: non-local, non-linear, singular and degenerative differential and functional-differential equations; non-classical problems of mathematical physics; qualitative properties of solutions; integral transformations.


Singular and quasi-linear parabolic and elliptic equations with singularities of Bessel operator type and non-linearities of $g(u)|\nabla u|^2$ kind are investigated. Necessary and sufficient conditions of stabilization of their solutions are found. Cauchy problem for differential-difference parabolic equations is investigated. Its classical unique solvability is proved, integral representation of its solution is obtained, asymptotic behaviour of that solution is investigated. Non-classical Cauchy problem for singular functional-differential parabolic equations, containing Bessel operators, translation operators and (integral) generalized translation operators, is investigated. Its classical unique solvability is proved, integral representation of its solution is obtained. Fourier–Bessel transforms of measures were studied. Estimates of $\Vert r^\mu\cdot\Vert_\infty\le C\Vert r^{\mu-1}\cdot\Vert_1}$ type are obtained for their weighted spherical means. Specified estimates are applied to the investigation of qualitative properties of solutions of singular differential and operator equations (including non-existence theorems).


Graduated from Faculty of Applied Mathematics and Mechanics of Voronezh State University (VSU) in 1983 (department of differentila equations). Ph.D. thesis was defended in 1986. A list of my works contains about 50 titles.

Main publications:
  • Muravnik A. B. On weighted norm estimates for mixed Fourier–Bessel transforms of non-negative functions // Pitman Res. Notes Math. Ser., 1997, 374, 119–123.
  • Muravnik A. B. Properties of stabilization functional for parabolic Cauchy problem // Progr. in Nonlin. Diff. Equations and Their Applications, 2000, 42, 217–221.
  • Muravnik A. B. Fourier–Bessel transformation of measures with several special variables and properties of singular differential equations // J. Korean Math. Soc., 2000, 37(6), 1043–1057.
  • Muravnik A. B. Fourier–Bessel transformation of compactly supported non-negative functions and estimates of solutions of singular differential equations // Functional Differential Equations, 2001, 8(3–4), 353–363.
  • Muravnik A. B. Fourier–Bessel transformation of measures and singular differential equations // North-Holland Math. Studies, 2001, 189, 335–345.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. A. B. Muravnik, “On qualitative properties of sign-constant solutions of some quasilinear parabolic problems”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 160 (2019),  85–94  mathnet  mathscinet
2. A. B. Muravnik, “Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics”, Mat. Zametki, 105:5 (2019),  747–762  mathnet  elib; Math. Notes, 105:5 (2019), 734–746  isi  scopus
3. A. B. Muravnik, “On qualitative properties of solutions to quasilinear parabolic equations admitting degenerations at infinity”, Ufimsk. Mat. Zh., 10:4 (2018),  77–84  mathnet; Ufa Math. J., 10:4 (2018), 77–84  isi  scopus
4. A. B. Muravnik, “Asymptotic properties of solutions of two-dimensional differential-difference elliptic problems”, CMFD, 63:4 (2017),  678–688  mathnet
5. A. B. Muravnik, “On the Dirichlet problem for differential-difference elliptic equations in a half-plane”, CMFD, 60 (2016),  102–113  mathnet
6. A. B. Muravnik, “Asymptotic Properties of Solutions of the Dirichlet Problem in the Half-Plane for Differential-Difference Elliptic Equations”, Mat. Zametki, 100:4 (2016),  566–576  mathnet  mathscinet  elib; Math. Notes, 100:4 (2016), 579–588  isi  scopus
7. A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem”, CMFD, 52 (2014),  3–141  mathnet; Journal of Mathematical Sciences, 216:3 (2016), 345–496
8. A. B. Muravnik, “On blow-up of solutions of some systems of quasilinear parabolic inequalities”, CMFD, 48 (2013),  84–92  mathnet; Journal of Mathematical Sciences, 202:6 (2014), 859–868  scopus
9. A. B. Muravnik, “On stabilization of solutions of singular elliptic equations”, Fundam. Prikl. Mat., 12:4 (2006),  169–186  mathnet  mathscinet  zmath  elib; J. Math. Sci., 150:5 (2008), 2408–2421  elib  scopus
10. A. B. Muravnik, “On asymptotics of solutions of parabolic equations with nonlocal high-order terms”, Tr. Semim. im. I. G. Petrovskogo, 25 (2006),  143–183  mathnet  mathscinet  zmath  elib; J. Math. Sci. (N. Y.), 135:1 (2006), 2695–2720  scopus
11. A. B. Muravnik, “On the Asymptotics of the Solution of the Cauchy Problem for Some Differential-Difference Parabolic Equations”, Differ. Uravn., 41:4 (2005),  538–548  mathnet  mathscinet; Differ. Equ., 41:4 (2005), 570–581
12. A. B. Muravnik, “Uniqueness of the solution of the Cauchy problem for some differential-difference parabolic equations”, Differ. Uravn., 40:10 (2004),  1385–1389  mathnet  mathscinet; Differ. Equ., 40:10 (2004), 1461–1466
13. A. B. Muravnik, “On the Unique Solvability of the Cauchy Problem for Some Difference-Differential Parabolic Equations”, Differ. Uravn., 40:5 (2004),  692–701  mathnet  mathscinet; Differ. Equ., 40:5 (2004), 742–752
14. A. B. Muravnik, “Stabilization of Solutions of Certain Singular Quasilinear Parabolic Equations”, Mat. Zametki, 74:6 (2003),  858–865  mathnet  mathscinet  zmath; Math. Notes, 74:6 (2003), 812–818  isi
15. A. B. Muravnik, “The Cauchy Problem for Certain Inhomogeneous Difference-Differential Parabolic Equations”, Mat. Zametki, 74:4 (2003),  538–548  mathnet  mathscinet  zmath  elib; Math. Notes, 74:4 (2003), 510–519  isi  scopus
16. V. N. Denisov, A. B. Muravnik, “On Stabilization of the Solution of the Cauchy Problem for Quasilinear Parabolic Equations”, Differ. Uravn., 38:3 (2002),  351–355  mathnet  mathscinet; Differ. Equ., 38:3 (2002), 369–374

Presentations in Math-Net.Ru
1. General-kind differential-difference elliptic equations in half-plane: asymptotic properties of solutions
Andrey Muravnik
New Trends in Mathematical and Theoretical Physics
October 7, 2016 17:40   
2. Задача Коши для параболических функционально-дифференциальных уравнений: интегральные представления и качественные свойства решений
A. B. Muravnik
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
February 16, 2011 16:00

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