Trudy Matematicheskogo Instituta imeni V.A. Steklova
 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 Mat. Inst. Steklova: Year: Volume: Issue: Page: Find

 Trudy 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

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, Trudy 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 Trudy 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 

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

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
•  Number of views: This page: 299 Full text: 72 References: 34