A Stefan problem for the heat equation subject to an integral condition

Elena Comparini; Domingo A. Tarzia

Rendiconti del Seminario Matematico della Università di Padova (1985)

  • Volume: 73, page 119-136
  • ISSN: 0041-8994

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Comparini, Elena, and Tarzia, Domingo A.. "A Stefan problem for the heat equation subject to an integral condition." Rendiconti del Seminario Matematico della Università di Padova 73 (1985): 119-136. <http://eudml.org/doc/107971>.

@article{Comparini1985,
author = {Comparini, Elena, Tarzia, Domingo A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {stability; Stefan problem; nonlinear integral equation; unique solution; contraction},
language = {eng},
pages = {119-136},
publisher = {Seminario Matematico of the University of Padua},
title = {A Stefan problem for the heat equation subject to an integral condition},
url = {http://eudml.org/doc/107971},
volume = {73},
year = {1985},
}

TY - JOUR
AU - Comparini, Elena
AU - Tarzia, Domingo A.
TI - A Stefan problem for the heat equation subject to an integral condition
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1985
PB - Seminario Matematico of the University of Padua
VL - 73
SP - 119
EP - 136
LA - eng
KW - stability; Stefan problem; nonlinear integral equation; unique solution; contraction
UR - http://eudml.org/doc/107971
ER -

References

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  1. [1] J.R. Cannon, The solution of the Heat Equation Subject to the Specification of Energy, Quart. Appl. Math., 21 (1963). Zbl0173.38404MR160437
  2. [2] N.I. Ionkin, Solution of a boundary value problem in heat conduction with a nonclassical boundary condition, Diff. Equation s, 13 (1977). Zbl0403.35043MR603291
  3. [3] J.R. Cannon - J. Van Der Hoek, The one phase Stefan Problem subject to the Specification of Energy, Jour. of Math. Anal. and Appl., 86 (1982). Zbl0508.35074MR649871
  4. [4] A. Friedmann, Free Boundary Problems for Parabolic Equations, I: Melting of Solids, Journal of Math. and Mec., 8, no. 4 (1959). Zbl0089.07801MR144078
  5. [5] B. Sherman, A. FreeBoundary Problem for the heat equation with prescribed flux at both fixed face and melting interface, Quart. Appl. Math., 25 (1967). Zbl0158.11904MR213104
  6. [6] J.R. Cannon - J. Van Der Hoek, The existence of and a continuous dependence result for the solution of the heat equation subject to the specification of energy, Suppl. B.U.M.I., 1 (1981). Zbl0538.35038MR641765
  7. [7] D.G. Schaefer, A new proof of the infinite differentiability of the Free Boundary in the Stefan Problem, Jour. ofDiff. Eq., 20 (1976). Zbl0314.35044MR390499
  8. [8] A. Fasano - M. Primicerio, Cauchy type free boundary problems for nonlinear parabolic equations, Riv. Mat. Univ. Parma, (4), 5 (1979). Zbl0699.35148MR584232
  9. [9] B. Sherman, Continuous Dependence and DifferentiabilityProperties of the Solution of a Free Boundary Problem for the Heat Equation, Quart. Appl. Math., 27 (1970). Zbl0191.39501MR509051
  10. [10] A. Fasano - M. Primicerio, La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente, I, Rend. Sem. Mat. Univ. Padova, 50 (1973). Zbl0278.35046MR366241
  11. [11] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'ceva, Linear and quasilinear equations of Parabolic Type, A.M.S. Tranl., 23 (1968). MR241822
  12. [12] A. Fasano - M. Primicerio, Free Boundary Problems for Nonlinear Parabolic Equations with Nonlinear Free Boundary Conditions, J. Math. Anal. Appl., 72 (1979). Zbl0421.35080MR552335
  13. [13] A. Friedmann, Partial Differential Equation of Parabolic Type, Prentice Hall, Englewood Cliffs, N.J. (1964). Zbl0144.34903
  14. [14] E. Comparini - R. Ricci - D.A. Tarzia, Remarks on a one-dimensional Stefan problem related to the diffusion-consumption model, to appear on Z.A.M.M. Zbl0558.76092MR778023
  15. [15] A. Fasano - M. Primicerio, General free-boundary problems for the heat equation, I, J. Math. Anal. Appl., 57, no. 3 (1977). Zbl0348.35047MR487016

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