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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 67–88 (Mi izv348)  

A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems

L. I. Kamynin, B. N. Khimchenko


Abstract: We consider two classes of second-order parabolic matrix-vector systems (with solutions $u\in M_{m\times 1}$, $m\geqslant 2$) that can be reduced to a single second-order parabolic equation for a scalar function $v=\langle p,u\rangle$, where $p\in M_{m\times 1}$ is a fixed stochastic constant vector. We consider the first boundary-value problem for a scalar second-order parabolic equation (with unbounded coefficients) in a domain unbounded with respect to $x$ under the assumption of strong absorption at infinity. We obtain an a priori estimate for solutions of the first boundary-value problem in the generalized Tikhonov–Täcklind classes. (The problem under investigation has at most one solution in these classes.)

DOI: https://doi.org/10.4213/im348

Full text: PDF file (1274 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2001, 65:4, 705–726

Bibliographic databases:

MSC: 35K50, 35B50, 35K20, 35B45, 35K15, 35A05, 35B05
Received: 27.09.1996

Citation: L. I. Kamynin, B. N. Khimchenko, “A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems”, Izv. RAN. Ser. Mat., 65:4 (2001), 67–88; Izv. Math., 65:4 (2001), 705–726

Citation in format AMSBIB
\Bibitem{KamKhi01}
\by L.~I.~Kamynin, B.~N.~Khimchenko
\paper A~priori estimates for the solution of the first boundary-value problem for a~class of second-order parabolic systems
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 67--88
\mathnet{http://mi.mathnet.ru/izv348}
\crossref{https://doi.org/10.4213/im348}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857711}
\zmath{https://zbmath.org/?q=an:1028.35028}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 705--726
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000348}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746823455}


Linking options:
  • http://mi.mathnet.ru/eng/izv348
  • https://doi.org/10.4213/im348
  • http://mi.mathnet.ru/eng/izv/v65/i4/p67

    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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:302
    Full text:116
    References:44
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019