Semigroup approach to the Stefan problem with non-linear flux

Enrico Magenes; Claudio Verdi; Augusto Visintin

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1983)

  • Volume: 75, Issue: 1-2, page 24-33
  • ISSN: 1120-6330

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Magenes, Enrico, Verdi, Claudio, and Visintin, Augusto. "Semigroup approach to the Stefan problem with non-linear flux." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 75.1-2 (1983): 24-33. <http://eudml.org/doc/287276>.

@article{Magenes1983,
author = {Magenes, Enrico, Verdi, Claudio, Visintin, Augusto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {nonlinear contraction semigroups; two-phase Stefan problem; nonlinear flux condition},
language = {eng},
month = {7},
number = {1-2},
pages = {24-33},
publisher = {Accademia Nazionale dei Lincei},
title = {Semigroup approach to the Stefan problem with non-linear flux},
url = {http://eudml.org/doc/287276},
volume = {75},
year = {1983},
}

TY - JOUR
AU - Magenes, Enrico
AU - Verdi, Claudio
AU - Visintin, Augusto
TI - Semigroup approach to the Stefan problem with non-linear flux
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1983/7//
PB - Accademia Nazionale dei Lincei
VL - 75
IS - 1-2
SP - 24
EP - 33
LA - eng
KW - nonlinear contraction semigroups; two-phase Stefan problem; nonlinear flux condition
UR - http://eudml.org/doc/287276
ER -

References

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  1. Bénilan, Ph. (1972) - Solutions intégrales d'équations d'évolution dans un espace de Banach. «C.R. Acad. Sc.», (A) 274, 47-50. Zbl0246.47068MR300164
  2. Bénilan, Ph. (1972) — Equations d'évolution dans un espace de Banach quelconque et applications. Thèse, Orsay. 
  3. Berger, A.E., Brezis, H., Rogers, C. W. (1979) - A numerical method for solving the problem u t Δ f ( u ) = 0 . «R.A.I.R.O. Num. Anal.», 13, 297-312. Zbl0426.65052MR555381
  4. Brezis, H., Strauss, W. A. (1973) - Semi-linear second-order elliptic equations in L 1 . «J. Math. Soc. Japan», 25, 565-590. Zbl0278.35041MR336050
  5. Cannon, J. R., Di Benedetto, E. (1980) - An n-dimensional Stefan problem with non-linear boundary conditions. «S.I.A.M. J. Math. Anal.», 11, 632-645. Zbl0459.35090MR579555DOI10.1137/0511058
  6. Crandall, M. G., Liggett, T. (1971) - Generation of semi-groups of non-linear transformation on general Banach spaces. «Amer. J. Math.», 93, 265-298. Zbl0226.47038MR287357
  7. Crandall, M. G., Pazy, A. (1972) - Nonlinear evolution equations in Banach spaces. «Israel J. Math.», 11, 57-94. Zbl0249.34049MR300166
  8. Damlamian, A. (1977) - Some results in the multiphase Stefan problem. «Comm. Partial Diff. Equat.», 2 (10), 1017-1044. Zbl0399.35054MR487015
  9. Evans, L. C. (1978) - Application of Non-linear Semigroup Theory to Certain Partial Differential Equations. In: «Nonlinear Evolution Equations», ed. M. C. Crandall, Academic Press. MR513818
  10. Ladyzenskaja, O., Ural'ceva, N. (1968) - Linear and quasilinear equations of elliptic type. Academic Press, New York. MR244627
  11. Lions, J. L., Magenes, E. (1972) - Non-homogeneous boundary value problems and application. Vol. I, Springer, Berlin. Zbl0223.35039MR350177
  12. Magenes, E. - Problemi di Stefan bifase in più variabili spaziali. To appear on «Le Matematiche». 
  13. Verdi, C. (1983) - On the numerical analysis of the Stefan problem with non-linear flux. Publ. I.A.N.-C.N.R. - Pavia, n. 372. 
  14. Niezgódka, M., Pawlow, I. (1983) - A generalized Stefan problem in several space variables. «Appl. Math. Optim.», 9, 193-224. Zbl0519.35079
  15. Visintin, A. (1981) — Sur le problème de Stefan avec flux non linéaire. «Boll. U.M.I., Anal. Funz. Appl.» (5), 18C (1), 63-86. Zbl0471.35078MR631569

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