Loading [MathJax]/jax/output/CommonHTML/jax.js
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
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


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 6, Pages 1006–1021
DOI: https://doi.org/10.31857/S0044466923060133 (Mi zvmmf11574) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

On critical exponents for weak solutions of the Cauchy problem for a (2+1)-dimensional nonlinear composite-type equation with gradient nonlinearity

M. O. Korpusova, A. K. Matveevaab

a Faculty of Physics, Lomonosov Moscow State University, 119992, Moscow, Russia
b National Engineering Physics Institute "MEPhI", 115409, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466923060133
Abstract: The Cauchy problem for a model nonlinear equation with gradient nonlinearity is considered. We prove the existence of two critical exponents, q1=2 and q2=3, such that this problem has no local-in-time weak (in some sense) solution for 1<q⩽q1, while such a solution exists for q>q1, but, for q1<q⩽q2, there is no global-in-time weak solution.
Key words: nonlinear Sobolev-type equations, blow-up, local solvability, nonlinear capacity, blow-up time estimates.
Funding agency Grant number
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
Russian Science Foundation 23-11-00056
This work was supported by the Foundation for Advancement of Theoretical Physics and Mathematics “BASIS” and by the Russian Science Foundation (project no. 23-11-00056), RUDN University.
Received: 04.05.2022
Revised: 22.12.2022
Accepted: 03.03.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 6, Pages 1070–1084
DOI: https://doi.org/10.1134/S096554252306012X
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: M. O. Korpusov, A. K. Matveeva, “On critical exponents for weak solutions of the Cauchy problem for a (2+1)-dimensional nonlinear composite-type equation with gradient nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 63:6 (2023), 1006–1021; Comput. Math. Math. Phys., 63:6 (2023), 1070–1084
Citation in format AMSBIB
\Bibitem{KorMat23}
\by M.~O.~Korpusov, A.~K.~Matveeva
\paper On critical exponents for weak solutions of the Cauchy problem for a $(2+1)$-dimensional nonlinear composite-type equation with gradient nonlinearity
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 6
\pages 1006--1021
\mathnet{http://mi.mathnet.ru/zvmmf11574}
\crossref{https://doi.org/10.31857/S0044466923060133}
\elib{https://elibrary.ru/item.asp?id=53836703}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 6
\pages 1070--1084
\crossref{https://doi.org/10.1134/S096554252306012X}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11574
  • https://www.mathnet.ru/eng/zvmmf/v63/i6/p1006
    • This publication is cited in the following 1 articles:
    1. A. N. Elmurodov, A. I. Sotvoldiyev, “A Diffusive Leslie–Gower Type Predator–Prey Model with Two Different Free Boundaries”, Lobachevskii J Math, 44:10 (2023), 4254  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:122
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025