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Matematicheskie Zametki, 2006, Volume 80, Issue 3, Pages 379–385
DOI: https://doi.org/10.4213/mzm2823 (Mi mzm2823) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Heat Distribution in an Infinite Rod

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (380 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm2823
Abstract: We construct an asymptotic expansion of the solution of the Cauchy problem for the one-dimensional heat equation for the case in which the initial function at infinity has power asymptotics.
Keywords: heat equation, Cauchy problem for the heat equation, heat distribution in an infinite rod, uniform asymptotics, Hermite function.
Received: 29.12.2005
English version:
Mathematical Notes, 2006, Volume 80, Issue 3, Pages 366–371
DOI: https://doi.org/10.1007/s11006-006-0148-x
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: S. V. Zakharov, “Heat Distribution in an Infinite Rod”, Mat. Zametki, 80:3 (2006), 379–385; Math. Notes, 80:3 (2006), 366–371
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm2823
  • https://doi.org/10.4213/mzm2823
  • https://www.mathnet.ru/eng/mzm/v80/i3/p379
    • This publication is cited in the following 10 articles:
    1. S. V. Zakharov, “Constructing the asymptotics of a solution of the heat equation from the known asymptotics of the initial function in three-dimensional space”, Sb. Math., 215:1 (2024), 101–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Sergey V. Zakharov, “The asymptotics of a solution of the multidimensional heat equation with unbounded initial data”, Ural Math. J., 7:1 (2021), 168–177  mathnet  crossref  mathscinet  zmath
    3. Zakharov S.V., “Long-Time Behavior of the Solution of the Cauchy Problem For the Third-Order Airy Equation”, Asymptotic Anal., 116:2 (2020), 139–148  crossref  mathscinet  isi  scopus
    4. S. V. Zakharov, “Asimptotika resheniya zadachi Koshi dlya evolyutsionnogo uravneniya Eiri na bolshikh vremenakh”, Funkts. analiz i ego pril., 53:3 (2019), 89–91  mathnet  crossref  mathscinet  elib
    5. S. V. Zakharov, “Asymptotics of the Solution of the Cauchy Problem for the Evolutionary Airy Equation at Large Times”, Funct Anal Its Appl, 53:3 (2019), 229  crossref
    6. S. V. Zakharov, “Two-parameter asymptotics in a bisingular Cauchy problem for a parabolic equation”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 191–200  mathnet  crossref  crossref  isi  elib
    7. S. V. Zakharov, “Asymptotic calculation of the heat distribution on a plane”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 243–249  mathnet  crossref  mathscinet  isi  elib
    8. S. V. Zakharov, “The Cauchy problem for a quasilinear parabolic equation with a large initial gradient and low viscosity”, Comput. Math. Math. Phys., 50:4 (2010), 665–672  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    9. Zakharov S.V., “Two-parameter asymptotics in the Cauchy problem for a quasi-linear parabolic equation”, Asymptot. Anal., 63:1-2 (2009), 49–54  mathscinet  zmath  isi  elib
    10. S. V. Zakharov, “The Cauchy problem for a quasilinear parabolic equation with two small parameters”, Dokl. Math., 78:2 (2008), 769–770  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
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