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Global-in-Time Asymptotic Solutions to Kolmogorov-Feller-Type Parabolic Pseudodifferential Equations with Small Parameter—Forward- and Backward-in-Time Motion
Abstract and Applied Analysis. 2013. P. 1-11.
We discuss the construction of inverse Couchy problem by using characteristics.
Springer, 2009
Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and ...
Added: February 20, 2013
Ludmila I. Kuzmina, Osipov Y., Vetoshkin N., International Journal for Computational Civil and Structural Engineering 2018 Vol. 14 No. 1 P. 92-101
The filtration problem in a porous medium is an important part of underground hydromechanics. Filtration of suspensions and colloids determines the processes of strengthening the soil and creating waterproof walls in the ground while building the foundations of buildings and underground structures. It is assumed that the formation of a deposit is dominated by the ...
Added: July 1, 2018
Л.И. Кузьмина, Осипов Ю. В., Вестник Московского государственного строительного университета 2014 № 7 С. 34-40
A classic pursuit problem is studied in which two material points - a Pursuer and a Pursued - move in a plane at constant speeds. The velocity vector of the Pursued does not change its direction and the velocity vector of the Pursuer turns and always aims at the Pursued. If the Pursuer moves at ...
Added: August 3, 2014
Blokh A., Oversteegen L., Ptacek R. et al., / Cornell University. Series math "arxiv.org". 2015.
Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we consider slices of the family of cubic invariant laminations defined by a fixed critical leaf with non-periodic endpoints. We parameterize each slice by ...
Added: February 11, 2015
Danilov V., Albeverio S., Russian Journal of Mathematical Physics 2011 Vol. 18 No. 1 P. 10-25
The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any ...
Added: April 12, 2012
L.I. Kuzmina, Osipov Y. V., Вестник Московского государственного строительного университета 2017 No. 11 P. 1278-1283
Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck ...
Added: January 6, 2018
Romaskevich O. L., L'Enseignement Mathématique 2014
We consider 3 -periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled with the complex law of reflection. ...
Added: December 25, 2014
Pardalos P. M., Rassias T. undefined., Springer, 2014
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional ...
Added: May 30, 2014
Kudryashova E., Leonov G. A., Kuznetsov N. V., IFAC-PapersOnLine 2015
In this paper an approach to modeling of the Tunisian social system in 2011–2014 is considered and the revolution, bifurcation, and controlled stabilization are discussed. Using statistical analysis of socio-economic indicators of Tunisia there are selected two bifurcation parameters, which have influenced on stability of socio-economic system of Tunisia. Based on this analysis the recommendations ...
Added: March 28, 2015
Aranson S. K., Belitsky G. R., Zhuzhoma E. V., American Mathematical Society, 1996
The book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achevements in this area obtained in recent times. The reader of this book need to be familiar only with basic courses in differential ...
Added: October 2, 2014
Demina M.V., Kudryashov N. A., Regular and Chaotic Dynamics 2016 Vol. 21 No. 3 P. 351-366
Polynomial dynamical systems describing interacting particles in the plane are
studied. A method replacing integration of a polynomial multi-particle dynamical system
by finding polynomial solutions of partial differential equations is introduced. The method
enables one to integrate a wide class of polynomial multi-particle dynamical systems. The
general solutions of certain dynamical systems related to linear second-order partial differential
equations are ...
Added: October 5, 2018
Pardalos P. M., Rassias T. undefined., Springer, 2014
This volume consists of chapters written by eminent scientists and engineers from the international community and presents significant advances in several theories, and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, and Discrete Mathematics and Geometry, as well as several ...
Added: May 30, 2014
Grushin V. V., Математические заметки 2017 Т. 102 № 6 С. 816-827
Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase. ...
Added: January 13, 2018
Gaydukov R., European Journal of Mechanics - B/Fluids 2021 Vol. 89 P. 401-410
An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow along a semi-infinite plate with small localized or periodic (fast-oscillating) irregularities on the surface whose shape depends on time. Numerical simulation of flow in the near-plate region is presented for two types of the shape change: oscillations of the ...
Added: January 4, 2021
Fonareva A. V., Gaydukov R. K., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 224-243
A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at ...
Added: March 22, 2021
V.L. Chernyshev, Minenkov D. S., Nazaikinskii V. E., Functional Analysis and Its Applications 2016 Vol. 50 No. 4 P. 291-307
We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. ...
Added: October 18, 2015
Filimonov D., Клепцын В. А., Nonlinearity 2014 Vol. 27 No. 6 P. 1205-1223
We study possible one-end finitely presented subgroups of <img />, acting without finite orbits. Our main result, theorem 1, establishes that any such action possesses the so-called property (<img />), that allows one to make distortion-controlled expansion and is thus sufficient to conclude that the action is Lebesgue-ergodic. We also propose a path towards full ...
Added: October 23, 2014
Blokh A., Oversteegen L., Ptacek R. et al., / Cornell University. Series math "arxiv.org". 2014.
A crucial fact established by Thurston in his 1985 preprint is that distinct \emph{minors} of quadratic laminations do not cross inside the unit disk; this led to his construction of a combinatorial model of the Mandelbrot set. Thurston's argument is based upon the fact that \emph{majors} of a quadratic lamination never enter the region between ...
Added: February 11, 2015
Mikheev A. V., Теория. Практика. Инновации 2017 № 9 (21)
In this paper we consider the calculation of a dynamical system described by a second-order differential equation in which a fundamental system of solutions consisting of functions of exponential type is replaced by bounded functions of the Verhulst model. The time dependence of the forces acting on the dynamical system is analyzed, and the obtained ...
Added: September 6, 2017
V.L. Chernyshev, Tolchennikov A. A., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 3 P. 290-298
In the problem of determining the asymptotics for the number of points moving along a metric tree, a polynomial approximation that uses Barnes’ multiple Bernoulli polynomials is found. The connection between the second term of the asymptotic expansion and the graph structure is discussed. ...
Added: October 3, 2017
Stankevich N., Kazakov A., Gonchenko S., Chaos 2020 Vol. 30 Article 123129
The generalized four-dimensional Rössler system is studied. Main bifurcation scenarios leading to a hyperchaos are described phenomenologically and their implementation in the model is demonstrated. In particular, we show that the formation of hyperchaotic invariant sets is related mainly to cascades (finite or infinite) of nondegenerate bifurcations of two types: period-doubling bifurcations of saddle cycles with a ...
Added: January 18, 2021
Smilga I., / Cornell University. Series arXiv "math". 2012. No. 1205.4442.
In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the Hölder exponent of such a function in a given point. From this formula, we deduce ...
Added: September 26, 2018
Romanov A., Izvestiya. Mathematics 2011 Vol. 75 No. 6 P. 1165-1183
For a linear contraction U in a Banach space X we discuss conditions for the convergence of ergodic operator nets corresponding to the adjoint operator U* in the W*O-topology of the space End X*. The accumulation points of all possible nets of this kind form a compact convex set L = Ker G in End ...
Added: October 6, 2012
Protasov V., Systems and Control Letters 2016 Vol. 90 P. 54-60
We prove the existence of positive linear switching systems (continuous time), whose trajectories grow to infinity, but slower than a given increasing function. This implies that, unlike the situation with linear ODE, the maximal growth of trajectories of linear systems may be arbitrarily slow. For systems generated by a finite set of matrices, this phenomenon ...
Added: February 22, 2016