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Fundam. Prikl. Mat., 2006, Volume 12, Issue 4, Pages 79–97 (Mi fpm960)  

This article is cited in 6 scientific papers (total in 6 papers)

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

V. N. Denisov


Abstract: In the paper, we study the sufficient conditions for the lower-order coefficient of the parabolic equation
$$ \Delta u+c(x,t)u-u_t=0 for x\in\mathbb R^N, t>0, $$
under which its solution satisfying the initial condition
$$ u|_{t=0}=u_0(x) for x\in \mathbb R^N, $$
stabilizes to zero, i.e., there exists the limit
$$ \lim_{t\to\infty}{u(x,t)}=0, $$
uniform in $x$ from every compact set $K$ in $\mathbb R^N$ for any function $u_0(x)$ belonging to a certain uniqueness class of the problem considered and growing not rapidly than $e^{a|x|^b}$ with $a>0$ and $b>0$ at infinity.

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English version:
Journal of Mathematical Sciences (New York), 2008, 150:6, 2344–2357

Bibliographic databases:

UDC: 517.955

Citation: V. N. Denisov, “On stabilization of solutions of the Cauchy problem for a parabolic equation with lower-order coefficients”, Fundam. Prikl. Mat., 12:4 (2006), 79–97; J. Math. Sci., 150:6 (2008), 2344–2357

Citation in format AMSBIB
\Bibitem{Den06}
\by V.~N.~Denisov
\paper On stabilization of solutions of the Cauchy problem for a~parabolic equation with lower-order coefficients
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 4
\pages 79--97
\mathnet{http://mi.mathnet.ru/fpm960}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314147}
\zmath{https://zbmath.org/?q=an:1151.35377}
\elib{https://elibrary.ru/item.asp?id=11143777}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 150
\issue 6
\pages 2344--2357
\crossref{https://doi.org/10.1007/s10958-008-0134-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42149146207}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Denisov V.N., “Stabilization of the solution to the cauchy problem for a parabolic equation with nonzero lower order coefficients in classes of increasing initial functions”, Dokl. Math., 81:1 (2010), 91–93  crossref  mathscinet  zmath  isi  elib  elib
    2. V. N. Denisov, “Sufficient conditions for stabilization of solutions of the Cauchy problem for nondivergent parabolic equations with lower-order coefficients”, Journal of Mathematical Sciences, 171:1 (2010), 46–57  mathnet  crossref  mathscinet
    3. V. N. Denisov, “Stabilization of a solution to the Cauchy problem for a nondivergence parabolic equation with growing lower order coefficients”, Proc. Steklov Inst. Math., 270 (2010), 91–103  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Denisov V.N., “Necessary and sufficient stabilization conditions for the solution of the Cauchy problem for a parabolic equation with nonzero lower order coefficients”, Dokl. Math., 82:1 (2010), 578–580  crossref  mathscinet  zmath  isi  elib  elib
    5. Denisov V.N., “Stabilization Conditions for the Solution of the Cauchy Problem for a Parabolic Equation with Growing Lower Order Coefficients”, Dokl. Math., 87:3 (2013), 348–350  crossref  mathscinet  zmath  isi  elib
    6. V. N. Denisov, “O povedenii pri bolshikh znacheniyakh vremeni reshenii parabolicheskikh uravnenii”, Uravneniya v chastnykh proizvodnykh, SMFN, 66, no. 1, Rossiiskii universitet druzhby narodov, M., 2020, 1–155  mathnet  crossref
  • Фундаментальная и прикладная математика
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