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Асимптотические решения волнового уравнения с вырождающейся скоростью.
С. 32–32.
Сипайло П. А.
Language:
Russian
In book
М.: Московский государственный институт электроники и математики, 2012.
Pelinovsky E., Капцов О. В., Доклады Российской академии наук. Физика, технические науки (ранее - Доклады Академии Наук. Физика) 2022 Т. 506 № 2 С. 46–51
Methods to obtain solutions describing traveling waves in strongly inhomogeneous media are discussed
within a linear wave equation with a variable speed (speed of sound). It is shown that there is a wide
range of propagation speed variations that allow for the existence of waves that do not reflect despite the
strong inhomogeneity of the medium. In this ...
Added: January 28, 2023
Beklaryan A., Бекларян Л. А., Журнал вычислительной математики и математической физики 2022 Т. 62 № 6 С. 933–950
The existence of a family of bounded soliton solutions for a finite-difference analogue of the wave equation with a general nonlinear potential is proved. The proof is based on a formalism establishing a one-to-one correspondence between soliton solutions of an infinite-dimensional dynamical system and solutions of a family of functional differential equations of the pointwise type. A key ...
Added: May 30, 2022
Beklaryan L. A., Beklaryan A., Computational Mathematics and Mathematical Physics 2021 Vol. 61 No. 12 P. 1980–1994
The existence of a family of bounded soliton solutions for a finite-difference wave equation with a quadratic potential is established. The proof is based on a formalism establishing a one-to-one correspondence between the soliton solutions of an infinite-dimensional dynamical system and the solutions of a family of functional differential equations of the pointwise type. A ...
Added: January 14, 2022
Бекларян Л. А., Beklaryan A., Журнал вычислительной математики и математической физики 2021 Т. 61 № 12 С. 2024–2039
The existence of a family of bounded soliton solutions for a finite difference wave equation with a quadratic potential is established. The proof is carried out within the framework of a formalism that establishes a one-to-one correspondence between soliton solutions of an infinite-dimensional dynamical system and solutions of a family of pointwise functional differential equations. For ...
Added: November 1, 2021
Maslov V., Теоретическая и математическая физика 2021 Т. 206 № 3 С. 448–452
We consider the construction of asymptotic solutions of linear equations related to equations of classical mechanics: the Hamilton–Jacobi equation and the transport equation. We show that these methods and also the theory of the mechanics of an infinitely narrow beam as a whole can be applied to some objects in bioenergy if the thin organic ...
Added: July 14, 2021
Zlotnik A., Kireeva O., / Series arXiv "math". 2020. No. arXiv:2011.14104v2[math.NA].
We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the classical Numerov approach and alternative technique based on averaging of the equation, together with further necessary improvements of the arising scheme for $n\geq 2$. The ...
Added: December 1, 2020
Petropavlovsky S., Цынков С. В., Журнал вычислительной математики и математической физики 2020 Т. 60 № 4 С. 725–737
A boundary method for simulation of wave propagation in 3D is proposed. The approach relies on the method of difference potentials and Huygens'principle allowing for an update of the solution only on the boundaries of a scatterer/ ...
Added: April 13, 2020
Romanov I., Шамаев А. С., Известия РАН. Теория и системы управления 2019 № 1 С. 109–116
The boundary controllability of oscillations of a plane membrane is studied. The magnitude
of the control is bounded. The controllability problem of driving the membrane to rest is considered.
The method of proof proposed in this paper can be applied to any dimension but only the two-dimensional case is considered for simplicity. ...
Added: April 30, 2019
Горшков А. А., Ossadtchi A., Фрадков А. Л., Информационно-управляющие системы 2017 Т. 5 № 90
Постановка проблемы: пространственное разрешение электроэнцефалографии/магнитоэнцефалографии зависит от метода решения обратной задачи, которая в силу фундаментальных физических причин является некорректно поставленной и имеет бесконечно большое количество решений. В последние несколько лет появились новые свидетельства о том, что нейрональная активность распространяется по коре в соответствии с волновым паттерном, характеризуемым некоторым направлением и скоростью распространения волны. Новые данные ...
Added: April 21, 2018
Vexler B., Zlotnik A., Trautmann P., Comptes Rendus Mathematique 2018 Vol. 356 No. 5 P. 523–531
The paper deals with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces of either measure-valued functions or vector measures. Bilinear finite element discretizations are constructed and their stability and error analysis is accomplished. ...
Added: April 8, 2017
Trautmann P., Vexler B., Zlotnik A., Mathematical Control and Related Fields 2018 Vol. 8 No. 2 P. 411–449
This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$ or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level ...
Added: April 8, 2017
Trautmann P., Vexler B., Zlotnik A., / Series "Working papers by Cornell University". 2017. No. 1702.00362.
This work is concerned with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L^2(I,\mathcal M(\Omega))$
or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$, $\alpha>0$. We construct and study three-level in time bilinear ...
Added: February 2, 2017
Dobrokhotov S. Y., Grushin V. V., Sergeev S. A. et al., Russian Journal of Mathematical Physics 2016 Vol. 23 No. 4 P. 455–474
A linear problem for propagation of gravity waves in the basin having the bottom of a form of a smooth background with added rapid oscillations is considered. The formulas derived below are asymptotic ones; they are quite formal, and we do not discuss the problem concerning their uniformness with respect to these parameters. ...
Added: December 12, 2016
Кузьмина Л.И., Осипов Ю. В., В кн.: Вопросы прикладной математики и вычислительной техники. Сборник трудовВып. 19.: М.: Издательский дом АСВ, 2016. С. 275–288.
The flow of monodispersed suspension in porous media with geometric capture mechanism of solid particles in filter pores is considered. Based on the integral representation of the solution the asymptotic solution of deep bed filtration problem near the concentration front is constructed and proved. ...
Added: September 11, 2016
Romanov I., Shamaev A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2016 Т. 470 № 1 С. 22–25
The boundary control of vibrations of a plane membrane is considered. A constraint is imposed on the absolute value of the control function. The goal of the control is to drive the membrane to rest. Exact mathematical definitions are given. The proof technique used in this paper can be applied to a membrane of any ...
Added: September 8, 2016
Кузьмина Л.И., Осипов Ю. В., Вестник Московского государственного строительного университета 2016 № 2 С. 49–61
The problem of filtering a suspension of tiny solid particles in a porous medium is con-sidered. The suspension with constant concentration of suspended particles at the filter inlet moves through the empty filter at a constant speed. There are no particles before the front; behind the front of the fluid flow solid particles interact with ...
Added: February 26, 2016
Кузьмина Л.И., Осипов Ю. В., В кн.: Вопросы прикладной математики и вычислительной механики: сборник научных трудовТ. 18.: М.: Издательство АСВ, 2015. С. 270–275.
Filtering the suspension in porous media is important for long-term assessment of the strength of soil in the construction of underground and hydraulic engineering structures. The geometrical and mechanical model of filtering is considered: solid particles pass freely through the larger pores, and get stuck at the entrance of tiny pores smaller than the diameter ...
Added: February 26, 2016
Л.И. Кузьмина, Осипов Ю. В., Вестник Московского государственного строительного университета 2015 № 1 С. 54–62
The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and ...
Added: February 9, 2015
Кузьмина Л.И., Осипов Ю. В., В кн.: Вопросы прикладной математики и вычислительной механики. Сборник научных трудовВып. 17.: М.: Национальный исследовательский Московский государственный строительный университет, 2014. С. 295–304.
A mathematical model of particle motion in the filter based on mechanical-geometrical interaction of particles with a porous medium is considered. Near the wave front an asymptotic solution of a quasi-linear system of partial differential equations for suspended and deposited particle concentrations is constructed. For a linear filtration coefficient asymptotics is compared with the exact ...
Added: September 7, 2014
Деркач М. М., Филимонов А. М., Filimonov D., М.: МИИТ, 2013.
В настоящем выпуске помещены методические указания к решению задач по разделу «Метод бегущих волн» дисциплины «Уравнения математической физики». В первой части настоящих методических указаний метод бегущих волн рассматривается применительно к одномерному волновому уравнению. Во второй части рассматриваются гиперболические системы довольно общего вида, поскольку метод бегущих волн можно с успехом распространить и на гиперболические системы уравнений ...
Added: January 9, 2014
Дмитриев М.Г., Сачков Ю. Л., Дифференциальные уравнения 2013 Т. 49 № 11 С. 1381–1389
В одной задаче оптимального управления, связанной с восстановлением поврежденного изображения, при регуляризации простейшего функционала энергии показывается, с помощью построения и анализа асимптотики решения соответствующей сингулярно возмущенной задачи, что оптимальное управление наряду с магистральным участком содержит и зоны быстрого изменения на границах интервала. ...
Added: November 15, 2013
Grushin V. V., Dobrokhotov S. Y., Сергеев С. А., Труды Математического института им. В.А. Стеклова РАН 2013 Т. 281 С. 170–187
We construct asymptotic solutions to the wave equation with velocity rapidly oscillating a smoothly varying background and with localized initial perturbations. First, using adiabatic approximation in the operator form, we perform homogenization that leads to a linearized Boussinesq-type equation with smooth coefficients and weak “anomalous” dispersion. Then, asymptotic solutions to this and, as a consequence, ...
Added: October 11, 2013
Manita L., Современная математика и ее приложения 2011 Т. 69
Рассматриваются задачи минимизации квадратичного функционала на траекториях волнового уравнения, которые на основе метода Фурье сводятся к задаче управления счетной системой обыкновенных дифференциальных уравнений. В качестве управления выступает плотность внешних сил. Исследуется проблема управляемости. ...
Added: October 7, 2013