Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, Volume 33, Issue 2, Pages 225–239
DOI: https://doi.org/10.35634/vm230203
(Mi vuu846)
 

MATHEMATICS

On multidimensional exact solutions of a nonlinear reaction–diffusion system

A. A. Kosova, È. I. Semenova, V. V. Tirskikhb

a Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences (ISDCT SB RAS), ul. Lermontova, 134, Irkutsk, 664033, Russia
b Irkutsk State Transport University, ul. Chernyshevskogo, 15, Irkutsk, 664074, Russia
References:
Abstract: We study a multidimensional case of a nonlinear reaction-diffusion system modeled by a system of two parabolic equations with power nonlinearities. Such systems can be used to simulate the process of propagation in space of interacting distributed formations of robots of two types. Such equations also describe the processes of nonlinear diffusion in reacting two-component continuous media. An original version of the reduction method is proposed, which reduces the construction of the dependence of the exact solution on spatial variables to the solution of the Helmholtz equation, and the dependence on time to the solution of a linear system of ordinary differential equations. A number of examples of multiparameter families of exact solutions given by elementary functions are constructed.
Keywords: reaction–diffusion system, reduction, exact solutions.
Funding agency Grant number
Russian Science Foundation 22-29-00819
The research was carried out with the financial support of the Russian Science Foundation, project no. 22-29-00819.
Received: 03.02.2023
Accepted: 04.04.2023
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 35K57, 35K55, 35Q35
Language: Russian
Citation: A. A. Kosov, È. I. Semenov, V. V. Tirskikh, “On multidimensional exact solutions of a nonlinear reaction–diffusion system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:2 (2023), 225–239
Citation in format AMSBIB
\Bibitem{KosSemTir23}
\by A.~A.~Kosov, \`E.~I.~Semenov, V.~V.~Tirskikh
\paper On multidimensional exact solutions of a nonlinear reaction--diffusion system
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2023
\vol 33
\issue 2
\pages 225--239
\mathnet{http://mi.mathnet.ru/vuu846}
\crossref{https://doi.org/10.35634/vm230203}
Linking options:
  • https://www.mathnet.ru/eng/vuu846
  • https://www.mathnet.ru/eng/vuu/v33/i2/p225
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Statistics & downloads:
    Abstract page:110
    Full-text PDF :34
    References:17
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024