Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Editorial staff
Guidelines for authors
License agreement
Editorial policy

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
Year:
Volume:
Issue:
Page:
Find




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

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2023, Volume 27, Number 2, Pages 375–383
DOI: https://doi.org/10.14498/vsgtu2012 (Mi vsgtu2012) 		 
Short Communication
Differential Equations and Mathematical Physics

Conditions for the existence and uniqueness of the solution of the Goursat problem for a system of equations with dominant partial derivatives

E. A. Sozontova

Elabuga Branch of Kazan (Volga Region) Federal University, Elabuga, 423600, Russian Federation
Full-text PDF (930 kB)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
PDF
HTML
DOI: https://doi.org/10.14498/vsgtu2012
Abstract: An $n$-dimensional system of equations with dominant partial derivatives of the $n$th order is being studied. The distinguishing feature of the considered system compared to other systems with partial derivatives is the presence of a first term in the equations on the right side of the system, representing a dominant derivative, while all other derivatives appearing in the system equations are obtained from it by discarding at least one differentiation with respect to any of the independent variables. The aim of the study is to find conditions for the unique solvability of the Goursat problem for the considered system. The main problem is reduced to a system of integral equations, the solution of which exists and is unique when the requirements of continuity of the kernels and right sides of this system are satisfied in the corresponding closed parallelepipeds of variable ranges. Conditions under which the main problem is uniquely solvable have been obtained. The final result in terms of the coefficients of the original system is formulated as a theorem.
Keywords: system of differential equations, Goursat problem, existence and uniqueness theorem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
The work was carried out at the expense of the Strategic Academic Leadership Program of Kazan (Volga Region) Federal University.
Received: March 21, 2023
Revised: May 13, 2023
Accepted: May 18, 2023
First online: June 20, 2023
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35G15
Language: Russian
Citation: E. A. Sozontova, “Conditions for the existence and uniqueness of the solution of the Goursat problem for a system of equations with dominant partial derivatives”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 27:2 (2023), 375–383
Citation in format AMSBIB
\Bibitem{Soz23}
\by E.~A.~Sozontova
\paper Conditions for the existence and uniqueness of the solution of the Goursat problem for a system of equations with dominant partial derivatives
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2023
\vol 27
\issue 2
\pages 375--383
\mathnet{http://mi.mathnet.ru/vsgtu2012}
\crossref{https://doi.org/10.14498/vsgtu2012}
\edn{https://elibrary.ru/MKLZCD}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu2012
  • https://www.mathnet.ru/eng/vsgtu/v227/i2/p375
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		������� ���������� ���������������� ������������ ������������. �����: ������-�������������� �����
    Statistics & downloads:
    Abstract page:282
    Full-text PDF :85
    References:131
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024