Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 196, Pages 36–43
DOI: https://doi.org/10.36535/0233-6723-2021-196-36-43
(Mi into847)
 

This article is cited in 1 scientific paper (total in 1 paper)

On solutions of the traveling wave type for the nonlinear heat equation

A. L. Kazakova, P. A. Kuznetsova, L. F. Spevakb

a Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
b Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg
Full-text PDF (182 kB) Citations (1)
References:
Abstract: In this paper, we consider the problem of finding solutions to a nonlinear heat equation with a power-law nonlinearity, which have the form of a traveling wave and simulate the propagation of disturbances along a cold background with a finite speed. We show that the construction can be reduced to the Cauchy problem for a second-order ordinary differential equation with a singular coefficient of the highest derivative. For this Cauchy problem, the theorem on the existence and uniqueness of a smooth solution is proved. We develop an algorithm for constructing an approximate solution based on the boundary-element method and also present the results of computational experiments with numerical estimates of the parameters of the solution.
Keywords: nonlinear heat equation, exact solution, existence theorem, uniqueness theorem, series, convergence, boundary-element method.
Funding agency Grant number
Russian Foundation for Basic Research 20-07-00407
20-51-S52003
This work was supported by the Russian Foundation for Basic Research and the Ministry of Science and Technology of Taiwan (project Nos. 20-07-00407 and 20-51-S52003).
Bibliographic databases:
Document Type: Article
UDC: 517.95, 519.62
MSC: 35K65
Language: Russian
Citation: A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “On solutions of the traveling wave type for the nonlinear heat equation”, Differential Equations and Optimal Control, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 196, VINITI, Moscow, 2021, 36–43
Citation in format AMSBIB
\Bibitem{KazKuzSpe21}
\by A.~L.~Kazakov, P.~A.~Kuznetsov, L.~F.~Spevak
\paper On solutions of the traveling wave type for the nonlinear heat equation
\inbook Differential Equations and Optimal Control
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 196
\pages 36--43
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into847}
\crossref{https://doi.org/10.36535/0233-6723-2021-196-36-43}
\elib{https://elibrary.ru/item.asp?id=46664221}
Linking options:
  • https://www.mathnet.ru/eng/into847
  • https://www.mathnet.ru/eng/into/v196/p36
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
    Statistics & downloads:
    Abstract page:167
    Full-text PDF :76
    References:24
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024