Green's function for the one-dimensional hyperbolic heat equation: remarks for global regularity

被引：2
作者：
Lopez Molina, J. A. [1 ]
机构：
[1] Univ Politecn Valencia, Dept Matemat Aplicada, ETS Ingn Agron & Medio Nat, Camino Vera, Valencia 46072, Spain
来源：
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA | 2020年 / 26卷 / 02期
关键词：
Hyperbolic heat equation; Sobolev spaces; Schwartz-Laplace transform; CONDUCTION; LEQUATION; SLAB;
D O I：
10.1007/s40590-019-00256-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We compute the Green's function for the Dirichlet problem associated with the hyperbolic heat equation in the spatial interval [0, 1]. This result is used as a counterexample about the global regularity of the solutions of the hyperbolic heat equation, showing that its Green's functions need not be continuous in all points of their domain. We apply this result to solve some mixed boundary value problems in hyperbolic heat theory.
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收藏
页码：657 / 671
页数：15
相关论文
共 18 条
  • [1] [Anonymous], 1986, Applied analysis
  • [2] Barletta A, 1996, HEAT MASS TRANSFER, V31, P443, DOI 10.1007/s002310050081
  • [3] Carey G. F., 1982, Numerical Heat Transfer, V5, P309, DOI 10.1080/10407788208913451
  • [4] CATTANEO C, 1958, CR HEBD ACAD SCI, V247, P431
  • [5] HYPERBOLIC HEAT CONDUCTION IN CATALYTIC SUPPORTED CRYSTALLITES
    CHAN, SH
    LOW, MJD
    MUELLER, WK
    [J]. AICHE JOURNAL, 1971, 17 (06) : 1499 - &
  • [6] Cho CJ, 2000, J KOREAN PHYS SOC, V36, P209
  • [7] Erdelyi A., 1954, Tables of integral transforms, VVol 2
  • [8] FLUX FORMULATION OF HYPERBOLIC HEAT-CONDUCTION
    FRANKEL, JI
    VICK, B
    OZISIK, MN
    [J]. JOURNAL OF APPLIED PHYSICS, 1985, 58 (09) : 3340 - 3345
  • [9] Lions J. L., 1968, PROBLEMES LIMITES NO, V2
  • [10] Lions JL., 1968, Problemes aux Limites Non Homogenes et Applications
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