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Matematicheskie Zametki, 2004, Volume 75, Issue 5, Pages 729–743
DOI: https://doi.org/10.4213/mzm71 (Mi mzm71) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On an Inverse Problem for a Parabolic Equation

D. S. Tkachenko

Moscow Engineering Physics Institute (State University)
Full-text PDF (245 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm71
Abstract: In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in $u$ in which the coefficients of $u_t$ and $u$ depend on $u_(x,t)$ , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established.
Received: 06.06.2002
English version:
Mathematical Notes, 2004, Volume 75, Issue 5, Pages 676–689
DOI: https://doi.org/10.1023/B:MATN.0000030976.63035.e1
Bibliographic databases:
UDC: 517.956.47
Language: Russian
Citation: D. S. Tkachenko, “On an Inverse Problem for a Parabolic Equation”, Mat. Zametki, 75:5 (2004), 729–743; Math. Notes, 75:5 (2004), 676–689
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm71
  • https://doi.org/10.4213/mzm71
  • https://www.mathnet.ru/eng/mzm/v75/i5/p729
    • This publication is cited in the following 3 articles:
    1. Dinh Nho Hao Bui Viet Huong Nguyen Thi Ngoc Oanh Phan Xuan Thanh, “Determination of a term in the right-hand side of parabolic equations”, J. Comput. Appl. Math., 309 (2017), 28–43  crossref  mathscinet  zmath  isi  scopus
    2. Erdem A., “An Adaptive Algorithm For Determination of Source Terms in a Linear Parabolic Problem”, J. Inverse Ill-Posed Probl., 22:4 (2014), 569–592  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Yaman M., “Blow-Up Solution and Stability to an Inverse Problem for a Pseudo-Parabolic Equation”, J. Inequal. Appl., 2012, 274  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    References:78
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