RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (191 kB)
References: PDF file   HTML file

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} 

• http://mi.mathnet.ru/eng/fpm960
• http://mi.mathnet.ru/eng/fpm/v12/i4/p79

 SHARE:

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
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
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
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
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
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
•  Number of views: This page: 313 Full text: 119 References: 36 First page: 1