https://journals.rudn.ru/CMFD/issue/feedContemporary Mathematics. Fundamental Directions2024-04-09T18:33:31+00:00Aleksandr L. Skubachevskiyskubachevskii-al@rudn.ruOpen Journal Systems<p><strong>Editor-in-Chief: </strong>Revaz V. Gamkrelidze, Academician of the Russian Academy of Sciences, Professor, Doctor of Physical and Mathematical Sciences</p> <p><strong>ISSN: </strong>2413-3639 (print), 2949-0618 (online). <strong>Founded in</strong> 2003 г. <span class="tlid-translation translation" lang="en"><strong>Publication frequency</strong>:</span> quarterly</p> <p><strong>Publisher: </strong> <a href="http://eng.rudn.ru/" target="_blank" rel="noopener noreferrer">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</a></p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Open Access</strong>: <img src="/files/journals/1//OA.png" alt="" width="68" height="25">. <strong>APC: </strong>no article processing charge</p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Peer-Review: </strong>blind </p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Publication language</strong>: Russian</p> <p style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><strong>Indexation</strong>: <a href="https://elibrary.ru/title_about.asp?id=9366" target="_blank" rel="noopener noreferrer">elibrary.ru</a>, <a href="http://www.mathnet.ru/php/journal.phtml?jrnid=cmfd&wshow=details&option_lang=eng" target="_blank" rel="noopener noreferrer">mathnet.ru,</a> <a href="http://scholar.google.ru/">Google Scholar</a>, Lens, Research4Life</p>https://journals.rudn.ru/CMFD/article/view/38692On the Boyarsky-Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift2024-04-09T18:16:19+00:00Yu. A. Alkhutovyurij-alkhutov@yandex.ruG. A. Chechkinchechkin@mech.math.msu.su<p>We establish the increased integrability of the gradient of the solution to the Dirichlet problem for the Laplace operator with lower terms and prove the unique solvability of this problem.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Alkhutov Y.A., Chechkin G.A.https://journals.rudn.ru/CMFD/article/view/38693On discrete models of Boltzmann-type kinetic equations2024-04-09T18:19:07+00:00A. V. Bobylevalexander.bobylev47@gmail.com<p>The known nonlinear kinetic equations, in particular, the wave kinetic equation and the quantum Nordheim–Uehling–Uhlenbeck equations are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the general Boltzmann-type kinetic equation that depends on a function of four real variables <span class="math inline">\(F(x,y; v,w)\)</span>. The function <span class="math inline">\(F\)</span> is assumed to satisfy certain simple relations. The main properties of this kinetic equation are studied. It is shown that the above mentioned specific kinetic equations correspond to different polynomial forms of the function <span class="math inline">\(F\)</span>. Then the problem of discretization of the general Boltzmann-type kinetic equation is considered on the basis of ideas similar to those used for construction of discrete velocity models of the Boltzmann equation. The main attention is paid to discrete models of the wave kinetic equation. It is shown that such models have a monotone functional similarly to the Boltzmann <span class="math inline">\(H\)</span>-function. The theorem of existence, uniqueness and convergence to equilibrium of solutions to the Cauchy problem with any positive initial conditions is formulated and discussed. The differences in long time behaviour between solutions of the wave kinetic equation and solutions of its discrete models are also briefly discussed.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Bobylev A.V.https://journals.rudn.ru/CMFD/article/view/38694The Sylvester problem and uniqueness sets in classes of entire functions2024-04-09T18:19:50+00:00G. G. Braichevbraichev@mail.ru<p>In this paper, we study the problem of finding, by a chosen sequence of complex numbers tending to infinity, the widest possible class of entire functions in a given scale for which this sequence is a uniqueness set. Within the framework of this general problem, we establish uniqueness theorems in various classes of entire functions, distinguished by restrictions on the type and indicator under a refined order. In particular, we complement the previously proven uniqueness theorem, using the concept of the Sylvester circle of the indicator diagram of an entire function of exponential type. We discuss the accuracy of the results obtained and their connection with known facts.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Braichev G.G.https://journals.rudn.ru/CMFD/article/view/38695The Riemann problem for the main model cases of the Euler-Poisson equations2024-04-09T18:20:44+00:00L. V. Gargyantsgargyants@bmstu.ruO. S. Rozanovarozanova@mech.math.msu.suM. K. TurzynskyM13041@yandex.ru<p>In this paper, we construct a solution to the Riemann problem for an inhomogeneous nonstrictly hyperbolic system of two equations, which is a corollary of the Euler-Poisson equations without pressure [9]. These equations can be considered for the cases of attractive and repulsive forces as well as for the cases of zero and nonzero underlying density background. The solution to the Riemann problem for each case is nonstandard and contains a delta-shaped singularity in the density component. In [16], solutions were constructed for the combination corresponding to the cold plasma model (repulsive force and nonzero background density). In this paper, we consider the three remaining cases.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Gargyants L.V., Rozanova O.S., Turzynsky M.K.https://journals.rudn.ru/CMFD/article/view/38696Averaging method for problems on quasiclassical asymptotics2024-04-09T18:21:36+00:00S. Yu. Dobrokhotovs.dobrokhotov@gmail.comV. E. Nazaikinskiinazaikinskii@yandex.ru<p>The averaging method is developed for operators with rapidly oscillating coefficients, intended for use in problems of quasiclassical asymptotics and not assuming a periodic structure of coefficient oscillations. Algebras of locally averaged functions are studied, an averaging theorem for differential operators of general form is proved, and some features of the method are illustrated using the example of the wave equation.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Dobrokhotov S.Y., Nazaikinskii V.E.https://journals.rudn.ru/CMFD/article/view/38697On limit cycles of autonomous systems2024-04-09T18:22:47+00:00T. M. Ivanovaivatatiana@gmail.comA. B. Kostinabkostin@yandex.ruA. I. Rubinshteinivatatiana@gmail.comV. B. Sherstyukovshervb73@gmail.com<p>We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential equations. We establish that any simple closed curve defined by the equation <span class="math inline">\(F(x,y)=1\)</span> with a sufficiently general function <span class="math inline">\(F\)</span> is a limit cycle for the corresponding autonomous system on the plane (and even for an infinite number of systems depending on the real parameter). These systems are written out explicitly. We analyze in detail several specific examples. Graphic illustrations are provided.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Ivanova T.M., Kostin A.B., Rubinshtein A.I., Sherstyukov V.B.https://journals.rudn.ru/CMFD/article/view/38698Coercive estimates for multilayer degenerate di erential operators2024-04-09T18:24:34+00:00G. G. Kazaryanhaikghazaryan@mail.ru<p>We obtain the conditions under which a given multilayer differential operator <span class="math inline">\(P(D)\)</span> (polynomial <span class="math inline">\(P(\xi)\)</span>) is more powerful than operator <span class="math inline">\(Q(D)\)</span> (polynomial <span class="math inline">\(Q(\xi)\)</span>). This is used to obtain estimates of monomials, which, in turn, using the theory of Fourier multipliers, is used to obtain coercive estimates of derivatives of functions through the differential operator <span class="math inline">\(P(D)\)</span> applied to these functions.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Kazaryan G.G.https://journals.rudn.ru/CMFD/article/view/38699On subordination conditions for systems of minimal di erential operators2024-04-09T18:27:22+00:00D. V. Limanskiid.limanskiy.dongu@mail.ruM. M. Malamudmalamud3m@gmail.com<p>In this paper, we provide a review of results on a priori estimates for systems of minimal differential operators in the scale of spaces <span class="math inline">\(L^p(\Omega),\)</span> where <span class="math inline">\(p\in[1,\infty].\)</span> We present results on the characterization of elliptic and <span class="math inline">\(l\)</span>-quasielliptic systems using a priori estimates in isotropic and anisotropic Sobolev spaces <span class="math inline">\(W_{p,0}^l(\mathbb R^n),\)</span> <span class="math inline">\(p\in[1,\infty].\)</span> For a given set <span class="math inline">\(l=(l_1,\dots,l_n)\in\mathbb N^n\)</span> we prove criteria for the existence of <span class="math inline">\(l\)</span>-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in <span class="math inline">\(W_{p,0}^l(\mathbb R^n),\)</span> <span class="math inline">\(p\in[1,\infty],\)</span> nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the <span class="math inline">\(L^\infty(\mathbb R^n)\)</span>-norm to the tensor product of two elliptic differential polynomials.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Limanskii D.V., Malamud M.M.https://journals.rudn.ru/CMFD/article/view/38700Lower average estimate for the minimum modulus on circles foran entire function of genus zero2024-04-09T18:30:56+00:00A. Yu. Popovaypopov.msu@yandex.ruV. B. Sherstyukovshervb73@gmail.com<p>The article was written based on the materials of the joint report of the authors, made by them at the Sixth International Conference “Functional spaces. Differential operators. Problems of mathematical education,” dedicated to the centenary of the birth of Corresponding Member of the Russian Academy of Sciences, Academician of the European Academy of Sciences L. D. Kudryavtsev. For an entire function represented by a canonical product of genus zero with positive roots, the following result is proved. For any <span class="math inline">\(\delta\in(0,1/3]\)</span>, the minimum modulus of such a function exceeds on average the maximum of its modulus raised to the power <span class="math inline">\(-1-\delta,\)</span> on any segment whose end ratio is equal to <span class="math inline">\(\exp( 2/\delta).\)</span> The main theorem is illustrated by two examples. The first of them shows that instead of the exponent <span class="math inline">\(-1-\delta\)</span> it is impossible to take <span class="math inline">\(-1.\)</span> The second example demonstrates the impossibility of replacing the value <span class="math inline">\(\exp(2/\delta)\)</span> by the value <span class="math inline">\(28/(15\delta)\)</span> in the theorem for small <span class="math inline">\(\delta.\)</span></p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Popov A.Y., Sherstyukov V.B.https://journals.rudn.ru/CMFD/article/view/38701To geometric aspects of in nite-dimensional dynamical systems2024-04-09T18:31:58+00:00V. M. Savchinsavchin-vm@rudn.ru<p style="text-align: justify;">The main goal of the work is to construct analogues of Christoffel symbols for infinitedimensional systems and on this basis to obtain geodesic equations for such systems. These analogies are of particular interest in terms of identifying the relationship between the dynamics of systems with an infinite number of degrees of freedom and Riemannian geometry, as well as geometry defined by the pseudo-Riemannian metric.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Savchin V.M.https://journals.rudn.ru/CMFD/article/view/38702On recovery of the solution to the Cauchy problem for the singular heat equation2024-04-09T18:33:31+00:00S. M. Sitniksitnik@bsu.edu.ruM. V. Polovinkinapolovinkina-marina@yandex.ruI. P. Polovinkinpolovinkin@yandex.ru<p>We present the results related to the solution of the problem of the best recovery of the solution to the Cauchy problem for the heat equation with the B-elliptic Laplace-Bessel operator in spatial variables from an exactly or approximately known finite set of temperature profiles.</p>2024-03-15T00:00:00+00:00Copyright (c) 2024 Sitnik S.M., Polovinkina M.V., Polovinkin I.P.