RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2005, Volume 248, Pages 46–51 (Mi tm117)  

Critical Exponents for Nondiagonal Quasilinear Parabolic Systems

K. O. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Using the method of nonlinear capacity (integral relations), critical exponents for the nonexistence of nontrivial nonnegative solutions are found for the Cauchy problem for systems of inequalities of the form $(u_i)_t-\operatorname {div} A_i(t,x,u_i,\nabla u_i)\ge b_i\prod _{j=1}^2 u_j^{Q_{ij}}+f_i$, where $Q_{ij}\ge 0$, $u_i=u_i(t,x)\ge 0$, $b_i=b_i(t,x)\ge 0$, and $f_i=f_i(t,x)\ge 0$, $x\in \mathbb R^N$, $t\ge 0$. Under additional assumptions concerning the functions $A_i$, a priori estimates and estimates of the lifespan of solutions are obtained in terms of the behavior of initial data and the functions $f_i$.

Full text: PDF file (165 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 248, 41–46

Bibliographic databases:
UDC: 517.9
Received in January 2005

Citation: K. O. Besov, “Critical Exponents for Nondiagonal Quasilinear Parabolic Systems”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 248, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 46–51; Proc. Steklov Inst. Math., 248 (2005), 41–46

Citation in format AMSBIB
\Bibitem{Bes05}
\by K.~O.~Besov
\paper Critical Exponents for Nondiagonal Quasilinear Parabolic Systems
\inbook Studies on function theory and differential equations
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 248
\pages 46--51
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm117}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2165914}
\zmath{https://zbmath.org/?q=an:1123.35094}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 248
\pages 41--46


Linking options:
  • http://mi.mathnet.ru/eng/tm117
  • http://mi.mathnet.ru/eng/tm/v248/p46

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  •    . . .  Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:288
    Full text:69
    References:33

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020