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CMFD, 2016, Volume 59, Pages 53–73 (Mi cmfd287)  

This article is cited in 2 scientific papers (total in 2 papers)

On the stabilization rate of solutions of the Cauchy problem for a parabolic equation with lower-order terms

V. N. Denisov

M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: For a parabolic equation in the half-space $\overline D=\mathbb R^N\times[0,\infty)$, $N\geqslant3$, we consider the Cauchy problem
\begin{gather*} L_1u\equiv Lu+c(x,t)u-u_t=0,\quad (x,t)\in D,
u(x,0)=u_0(x),\quad x\in\mathbb R^N. \end{gather*}
Depending on estimates on the coefficient $c(x,t),$ we establish power or exponential rate of stabilization of solutions of the Cauchy problem равномерно по $x$ на каждом компакте $K$ в $\mathbb R^N$ для произвольной ограниченной непрерывной в $\mathbb R^N$ начальной функции $u_0(x)$.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00471


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UDC: 517.956.4

Citation: V. N. Denisov, “On the stabilization rate of solutions of the Cauchy problem for a parabolic equation with lower-order terms”, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, CMFD, 59, PFUR, M., 2016, 53–73

Citation in format AMSBIB
\Bibitem{Den16}
\by V.~N.~Denisov
\paper On the stabilization rate of solutions of the Cauchy problem for a~parabolic equation with lower-order terms
\inbook Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22--29, 2014). Part~2
\serial CMFD
\yr 2016
\vol 59
\pages 53--73
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd287}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. N. Denisov, “O skorosti stabilizatsii resheniya zadachi Koshi dlya nedivergentnykh parabolicheskikh uravnenii s rastuschim mladshim koeffitsientom”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 4, Rossiiskii universitet druzhby narodov, M., 2017, 586–598  mathnet  crossref
    2. V. N. Denisov, “On long-time asymptotics of solutions of parabolic equations with increasing leading coefficients”, Dokl. Math., 96:1 (2017), 308–311  crossref  mathscinet  zmath  isi  elib  scopus
  • Современная математика. Фундаментальные направления
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