The paper is devoted to the study of a singular nonlinear second-order parabolic equation, which is called the porous medium equation or the nonlinear heat equation. One of the important classes of its solutions is he...
The paper is devoted to the study of a singular nonlinear second-order parabolic equation, which is called the porous medium equation or the nonlinear heat equation. One of the important classes of its solutions is heat waves propagating over a zero background with a finite velocity. This property is not typical for parabolic equations and is a consequence of singularity. The main object of study is exact solutions of mentioned type. A new way of separating variables is used to represent them. We obtain conditions when it is possible to make a reduction to the Cauchy problem for an ordinary second-order differential equation with a singularity. It is shown that the Cauchy problem describes a heat wave whose front moves exponentially. We construct a solution to the Cauchy problem as a power series and determine the cases when the series breaks off, i.e. the solution has the form of a polynomial, and the corresponding heat wave can be written explicitly. If the Cauchy problem cannot be explicitly integrated, the solution is constructed numerically. An algorithm based on the boundary element method is proposed. We perform a computational experiment and conclude the properties of the found solutions. Besides, the accuracy of the calculation results is analyzed.
The paper addresses a nonlinear heat equation (the porous medium equation) in the case of a power-law dependence of the heat conductivity coefficient on temperature. The equation is used for describing high-temperatur...
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The data collected during various kinds of scientific research may be represented both by well known binary file formats and by custom formats specially developed for some unique device. While thorough understanding o...
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We have developed the Hamiltonian theory for collective longitudinally polarized colorless excitations (plasmons) in a high-temperature gluon plasma using the general formalism for constructing the wave theory in nonl...
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Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these nu...
We present a cloud storage for collaborations of small and medium-sized experiments in the field of particle astrophysics. This storage provides a unified interface for accessing data from different experiments. In th...
We present a cloud storage for collaborations of small and medium-sized experiments in the field of particle astrophysics. This storage provides a unified interface for accessing data from different experiments. In this article, we will focus on the capabilities of the storage for processing user requests for data, as well as on some technical details of the implementation of data selection. We have deployed a working prototype of the storage. Currently the prototype integrates data from such astrophysical experiments as TAIGA and KASCADE. As a result, users of the respective collaborations have the opportunity to collect scientific data from different experiments seamlessly within one request to conduct joint data analysis.
Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a meth...
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The paper addresses the research of the large-scale penetration of renewable energy into the power system of Vietnam. The proposed approach presents the optimization of operational decisions in different power generat...
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The article considers information technologies for monitoring pollution of lake systems. The authors created a geoportal that provides collection and generalization of the results of researches of anthropogenic impact...
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