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Journal of Siberian Federal University. Mathematics & Physics, 2014, Volume 7, Issue 2, Pages 173–185 (Mi jsfu367)  
This article is cited in 5 scientific papers (total in 5 papers)

On the existence of solution of some problems for nonlinear loaded parabolic equations with Cauchy data

Igor V. Frolenkov, Maria A. Darzhaa

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041 Russia
Full-text PDF (202 kB) Citations (5)
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Abstract: Two problems are considered in this paper. First problem is the Cauchy problem for a two-dimensional loaded parabolic equation with coefficients dependent on unknown function and its derivatives. Second problem is the Cauchy problem for one-dimensional equation of the Burgers-type. The sufficient conditions of the existence of solutions of these problems in classes of smooth bounded functions are presented in the paper. The method of weak approximation is used for the purpose of obtaining the proof.
Keywords: inverse problem, direct problem, loaded equation, parabolic equation, equation of the Burgers-type, method of weak approximation.
Received: 22.10.2013
Received in revised form: 25.12.2013
Accepted: 17.02.2014
Document Type: Article
UDC: 517.9
Language: English
Citation: Igor V. Frolenkov, Maria A. Darzhaa, “On the existence of solution of some problems for nonlinear loaded parabolic equations with Cauchy data”, J. Sib. Fed. Univ. Math. Phys., 7:2 (2014), 173–185
Citation in format AMSBIB
\Bibitem{FroDar14}
\by Igor~V.~Frolenkov, Maria~A.~Darzhaa
\paper On the existence of solution of some problems for nonlinear loaded parabolic equations with Cauchy data
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 2
\pages 173--185
\mathnet{http://mi.mathnet.ru/jsfu367}
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  • https://www.mathnet.ru/eng/jsfu367
  • https://www.mathnet.ru/eng/jsfu/v7/i2/p173
    • This publication is cited in the following 5 articles:
    1. Igor V. Frolenkov, Roman V. Sorokin, Ivan E. Zubrov, “On the solvability of Burgers-type equation with special type of non-linearity”, Zhurn. SFU. Ser. Matem. i fiz., 16:5 (2023), 690–699  mathnet
    2. Igor V. Frolenkov, Irina S. Antipina, Natalya M. Terskikh, “On uniqueness and continuous dependence on the initial data of the solution of a system of two loaded parabolic equations with the Cauchy data”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 298–309  mathnet  crossref
    3. I. V. Frolenkov, E. N. Kriger, “On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations”, J. Math. Sci. (N. Y.), 254:6 (2021), 743–760  mathnet  crossref  mathscinet
    4. I. V. Frolenkov, M. A. Yarovaya, “On the Cauchy problem for a one-dimensional loaded parabolic equation of a special form”, J. Math. Sci. (N. Y.), 254:6 (2021), 761–775  mathnet  crossref  mathscinet
    5. Galina V. Romanenko, Igor V. Frolenkov, “On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data”, Zhurn. SFU. Ser. Matem. i fiz., 9:3 (2016), 364–373  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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