Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A one-phase hyperbolic Stefan problem in multi-dimensional space

Author: De Ning Li
Journal: Trans. Amer. Math. Soc. 318 (1990), 401-415
MSC: Primary 35R35; Secondary 80A20
MathSciNet review: 1005936
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The hyperbolic heat transfer model is obtained by replacing the classical Fourier's law with the relaxation relation $ \tau \vec qt + \vec q = - k\nabla T$. The sufficient and necessary conditions are derived for the local existence and uniqueness of classical solutions for multi- $ {\text{D}}$ Stefan problem of hyperbolic heat transfer model where phase change is accompanied with delay of latent heat storage.

References [Enhancements On Off] (What's this?)

  • [1] A. T. Bui and D. Li, Double shock fronts for hyperbolic systems of conservation laws in multidimensional space, Trans. Amer. Math. Soc. 316 (1989), 233-250. MR 935939 (91b:35072)
  • [2] A. Friedman and B. Hu, The Stefan problem for a hyperbolic heat equation, IMA Preprint 348, 1987. MR 988334 (90d:35307)
  • [3] L. Gårding, Le problème de la dérivée oblique pour l'équation des ondes, C. R. Acad Sci. Paris Sér. A-B 285 (1977), 773-775. MR 0458511 (56:16711)
  • [4] J. Greenberg, A hyperbolic heat transfer problem with phase changes, IMA J. Appl. Math. 38 (1987), 1-21. MR 983526 (90d:80002)
  • [5] M. Ikawa, A mixed problem for hyperbolic equations of second order with a first order derivative boundary condition, Publ. R.I.M.S. Kyoto Univ. 5 (1969), 119-147. MR 0277890 (43:3623)
  • [6] D. D. Joseph and Luigi Preziosi, Heat waves, Rev. Modern Phys. 61 (1989), 41-73. MR 977943 (89k:80001)
  • [7] T. Kato, The Cauchy problem for quasilinear symmetric hyperbolic systems, Arch. Rational Mech. Anal. 58 (1975), 181-205. MR 0390516 (52:11341)
  • [8] D. Li, Nonlinear initial-boundary value problem and the existence of multi-dimensional shock wave for quasilinear hyperbolic-parabolic coupled systems, Chinese Ann. Math. 8B (1987), 252-280. MR 901389 (89d:35114)
  • [9] -, The well-posedness of a hyperbolic Stefan problem, Quart. Appl. Math. 47 (1989), 221-231. MR 998097 (90m:35207)
  • [10] A. Majda, The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc. 275 (1983). MR 699241 (85f:35139)
  • [11] A. Majda and E. Thomann, Multi-dimensional shock fronts for second order wave equations, Comm. Partial Differential Equations 12 (1987), 777-828. MR 890631 (88k:35130)
  • [12] S. Miyatake, Mixed problem for hyperbolic equation of second order, J. Math. Kyoto Univ. 13 (1973), 435-487. MR 0333467 (48:11792)
  • [13] J. Rauch and F. Massey, Differentiability for solutions to hyperbolic initial-boundary value problems, Trans. Amer. Math. Soc. 189 (1974), 303-318. MR 0340832 (49:5582)
  • [14] R. E. Showalter and N. J. Walkington, A hyperbolic Stefan problem, Quart. Appl. Math. 45 (1987), 769-782. MR 917025 (89d:35190)
  • [15] A. Solomon, V. Alexiades, D. Wilson and J. Drake, On the formulation of a hyperbolic Stefan problem, Quart. Appl. Math. 43 (1985), 295-304. MR 814228 (87c:80018)
  • [16] A. Solomon, V. Alexiades, D. Wilson and J. Greenberg, A hyperbolic Stefan problem with discontinuous temperature, ORNL-6216, March, 1986.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35R35, 80A20

Retrieve articles in all journals with MSC: 35R35, 80A20

Additional Information

Keywords: Hyperbolic equation, heat transfer, Stefan problem
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society