Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






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


Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 1, Pages 119–129 (Mi timm1035)  

This article is cited in 16 scientific papers (total in 16 papers)

On a degenerate boundary value problem for the porous medium equation in spherical coordinates

A. L. Kazakova, P. A. Kuznetsovb, L. F. Spevakc

a Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
b Institute of Mathematics, Economics and Informatics of Irkutsk State University
c Institute of Engineering Science, Urals Branch, Russian Academy of Sciences
References:
Abstract: We study a degenerate boundary value problem for the porous medium equation in the case of spherical coordinates. The results of this study can be applied to the problem of heat propagation in a neighborhood of a closed spherical surface. For the boundary value problem, we prove the existence and uniqueness theorem for solutions in the class of analytical functions and propose a numerical method for constructing solutions based on the boundary element approach. We use both truncated series and the proposed numerical method to carry out sample computations.
Keywords: porous medium equation, boundary value problem, analytical solution, boundary element method.
Received: 18.04.2013
Bibliographic databases:
Document Type: Article
UDC: 517.95+518.517
Language: Russian
Citation: A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “On a degenerate boundary value problem for the porous medium equation in spherical coordinates”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 119–129
Citation in format AMSBIB
\Bibitem{KazKuzSpe14}
\by A.~L.~Kazakov, P.~A.~Kuznetsov, L.~F.~Spevak
\paper On a~degenerate boundary value problem for the porous medium equation in spherical coordinates
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 1
\pages 119--129
\mathnet{http://mi.mathnet.ru/timm1035}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364197}
\elib{https://elibrary.ru/item.asp?id=21258488}
Linking options:
  • https://www.mathnet.ru/eng/timm1035
  • https://www.mathnet.ru/eng/timm/v20/i1/p119
  • This publication is cited in the following 16 articles:
    1. S. A. Zinina, A. I. Popov, A. V. Eremin, “Chislennoe reshenie nelineinoi zadachi teploprovodnosti v poristoi plastine s uporyadochennoi makrostrukturoi”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2024, no. 1, 53–67  mathnet  crossref  elib
    2. P. A. Kuznetsov, “Analiticheskie diffuzionnye volny v nelineinoi parabolicheskoi modeli “khischnik - zhertva””, Tr. IMM UrO RAN, 28, no. 2, 2022, 158–167  mathnet  crossref  mathscinet  elib
    3. A. L. Kazakov, A. A. Lempert, “Tochnye resheniya tipa diffuzionnykh voln dlya nelineinogo vyrozhdayuschegosya parabolicheskogo uravneniya vtorogo poryadka”, Tr. IMM UrO RAN, 28, no. 3, 2022, 114–128  mathnet  crossref  elib
    4. A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “O resheniyakh tipa beguschei volny dlya nelineinogo uravneniya teploprovodnosti”, Differentsialnye uravneniya i optimalnoe upravlenie, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 196, VINITI RAN, M., 2021, 36–43  mathnet  crossref  elib
    5. A. L. Kazakov, L. F. Spevak, “Priblizhennye i tochnye resheniya vyrozhdayuschegosya nelineinogo uravneniya teploprovodnosti s proizvolnoi nelineinostyu”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 34 (2020), 18–34  mathnet  crossref
    6. Kazakov A.L. Kuznetsov P.A., “Exact Solutions of the Nonlinear Heat Conduction Model”, Bull. South Ural State U. Ser.-Math Model Program Comput., 13:4 (2020), 33–47  crossref  zmath  isi  scopus
    7. A. L. Kazakov, “Construction and investigation of exact solutions with free boundary to a nonlinear heat equation with source”, Siberian Adv. Math., 30:2 (2020), 91–105  mathnet  crossref  crossref
    8. A. L. Kazakov, O. A. Nefedova, L. F. Spevak, “Solution of the problem of initiating the heat wave for a nonlinear heat conduction equation using the boundary element method”, Comput. Math. Math. Phys., 59:6 (2019), 1015–1029  mathnet  crossref  crossref  isi  elib
    9. A. L. Kazakov, P. A. Kuznetsov, “Ob analiticheskikh resheniyakh zadachi o dvizhenii teplovogo fronta dlya nelineinogo uravneniya teploprovodnosti s istochnikom”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 24 (2018), 37–50  mathnet  crossref
    10. A. L. Kazakov, P. A. Kuznetsov, “On the analytic solutions of a special boundary value problem for a nonlinear heat equation in polar coordinates”, J. Appl. Industr. Math., 12:2 (2018), 255–263  mathnet  crossref  crossref  elib  elib
    11. A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “Trekhmernaya teplovaya volna, porozhdennaya kraevym rezhimom, zadannym na podvizhnom mnogoobrazii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 16–34  mathnet  crossref
    12. A. L. Kazakov, Sv. S. Orlov, “O nekotorykh tochnykh resheniyakh nelineinogo uravneniya teploprovodnosti”, Tr. IMM UrO RAN, 22, no. 1, 2016, 112–123  mathnet  mathscinet  elib
    13. A. L. Kazakov, L. F. Spevak, O. A. Nefedova, “Reshenie dvumernoi zadachi o dvizhenii fronta teplovoi volny s ispolzovaniem stepennykh ryadov i metoda granichnykh elementov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 18 (2016), 21–37  mathnet
    14. A. L. Kazakov, P. A. Kuznetsov, A. A. Lempert, “O postroenii teplovoi volny dlya nelineinogo uravneniya teploprovodnosti v simmetrichnom sluchae”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 11 (2015), 39–53  mathnet
    15. A. L. Kazakov, L. F. Spevak, “Chislennoe i analiticheskoe issledovanie nekotorykh protsessov, opisyvaemykh nelineinym uravneniem teploprovodnosti”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2015, 42–48  mathnet  elib
    16. P. A. Kuznetsov, “O kraevoi zadache s vyrozhdeniem dlya nelineinogo uravneniya teploprovodnosti s dannymi na zamknutoi poverkhnosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 9 (2014), 61–74  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:547
    Full-text PDF :169
    References:98
    First page:21
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025