RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



J. Sib. Fed. Univ. Math. Phys.:
Year:
Volume:
Issue:
Page:
Find






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


J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 3, Pages 337–348 (Mi jsfu264)  

This article is cited in 5 scientific papers (total in 5 papers)

On an ill-posed problem for the heat equation

Roman E. Puzyrev, Alexander A. Shlapunov

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: A boundary value problem for the heat equation is studied. It consists of recovering a function, satisfying the heat equation in a cylindrical domain, via its values ant the values of its normal derivative on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding Hölder spaces; besides, additional initial data do not turn the problem to a well-posed one. Using Integral Representation's Method we obtain Uniqueness Theorem and solvability conditions for the problem.

Keywords: boundary value problems for heat equation, ill-posed problems, integral representation's method.

Full text: PDF file (255 kB)
References: PDF file   HTML file
UDC: 517.956.4
Received: 10.01.2012
Received in revised form: 10.02.2012
Accepted: 20.04.2012
Language:

Citation: Roman E. Puzyrev, Alexander A. Shlapunov, “On an ill-posed problem for the heat equation”, J. Sib. Fed. Univ. Math. Phys., 5:3 (2012), 337–348

Citation in format AMSBIB
\Bibitem{PuzShl12}
\by Roman~E.~Puzyrev, Alexander~A.~Shlapunov
\paper On an ill-posed problem for the heat equation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 3
\pages 337--348
\mathnet{http://mi.mathnet.ru/jsfu264}


Linking options:
  • http://mi.mathnet.ru/eng/jsfu264
  • http://mi.mathnet.ru/eng/jsfu/v5/i3/p337

    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

    This publication is cited in the following articles:
    1. Becache E., Bourgeois L., Franceschini L., Darde J., “Application of Mixed Formulations of Quasi-Reversibility To Solve Ill-Posed Problems For Heat and Wave Equations: the 1D Case”, Inverse Probl. Imaging, 9:4 (2015), 971–1002  crossref  mathscinet  zmath  isi  scopus
    2. J. Darde, “Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems”, Inverse Probl. Imaging, 10:2 (2016), 379–407  crossref  mathscinet  zmath  isi  scopus
    3. K. O. Makhmudov, O. I. Makhmudov, N. N. Tarkhanov, “A Nonstandard Cauchy Problem for the Heat Equation”, Math. Notes, 102:2 (2017), 250–260  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Ilya A. Kurilenko, Alexander A. Shlapunov, “On Carleman-type formulas for solutions to the heat equation”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 421–433  mathnet  crossref
    5. I. E. Niezov, “Regulyarizatsiya nestandartnoi zadachi Koshi dlya dinamicheskoi sistemy Lame”, Izv. vuzov. Matem., 2020, no. 4, 54–63  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
    Number of views:
    This page:201
    Full text:91
    References:24

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021