Some new results on a Stefan problem in a concentrated capacity

Enrico Magenes

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1992)

  • Volume: 3, Issue: 1, page 23-34
  • ISSN: 1120-6330

Abstract

top
An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.

How to cite

top

Magenes, Enrico. "Some new results on a Stefan problem in a concentrated capacity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.1 (1992): 23-34. <http://eudml.org/doc/244110>.

@article{Magenes1992,
abstract = {An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.},
author = {Magenes, Enrico},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Nonlinear parabolic partial differential equations; Heat conduction; Phase changes; Stefan problem; Laplace-Beltrami operator; phase change process; concentrated capacity; existence; uniqueness; regularized solutions; compactness argument; weak solution},
language = {eng},
month = {3},
number = {1},
pages = {23-34},
publisher = {Accademia Nazionale dei Lincei},
title = {Some new results on a Stefan problem in a concentrated capacity},
url = {http://eudml.org/doc/244110},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Magenes, Enrico
TI - Some new results on a Stefan problem in a concentrated capacity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/3//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 1
SP - 23
EP - 34
AB - An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.
LA - eng
KW - Nonlinear parabolic partial differential equations; Heat conduction; Phase changes; Stefan problem; Laplace-Beltrami operator; phase change process; concentrated capacity; existence; uniqueness; regularized solutions; compactness argument; weak solution
UR - http://eudml.org/doc/244110
ER -

References

top
  1. ANDREUCCI, D., Existence and uniqueness of solution to a concentrated capacity problem with change of phase. Europ. J. of Appl. Math., 1, 1990, 339-351. Zbl0734.35161MR1117356DOI10.1017/S0956792500000280
  2. BREZZI, F., Sul metodo di penalizzazione per operatori parabolici. Rend. Ist. Lombardo, Sc., A 107, 1973, 241-256. Zbl0301.35044MR352706
  3. DE RHAM, G., Variétés differentiables. Hermann & C., Paris1955. Zbl0065.32401
  4. FASANO, A. - PRIMICERIO, M. - RUBINSTEIN, L., A model problem for heat conduction with a free boundary in a concentrated capacity. J. Inst. Maths. Applics., 26, 1980, 327-347. Zbl0456.35093MR605396
  5. LADYZHENSKAYA, O. - SOLONNIKOV, V. - URALZEVA, N., Linear and quasi-linear equations of parabolic type. Amer. Math. Soc. Transl., 23, 1968. Zbl0174.15403
  6. LIONS, J. L. - MAGENES, E., Non homogeneous boundary value problems and applications. Vols. 1 and 2, Springer Verlag, Berlin1972. Zbl0223.35039
  7. MAGENES, E., Numerical approximation of non linear evolution problems. In: P. DAUTRAY (ed.), Frontiers in Pure and Applied Mathematics. Proc. Conf. in honour of J. L. Lions, Elsevier, Amsterdam1991, 193-207. Zbl0744.65095MR1110601
  8. MAGENES, E., On a Stefan problem on the boundary of a domain. Proceedings of the Intern. Meeting on Partial Differential Equations and related Problems (in honour to L. Nirenberg) (Trento, Sept. 3/8, 1990). To appear. Zbl0803.35170MR1190942
  9. MAGENES, E., On a Stefan problem in a concentrated capacity. Nonlinear Analysis (A tribute in honour of Giovanni Prodi), Scuola Normale Superiore, Pisa, 1991, 217-229. Zbl0839.35151MR1205385
  10. SHILLOR, M., Existence and continuity of a weak solution to the problem of a free boundary in a concentrated capacity. Proc. Roy. Soc. Edinburgh, Sect. A, 100, 1985, 271-280. Zbl0591.35086MR807706DOI10.1017/S0308210500013810
  11. TOMARELLI, F., Weak solution for an abstract Cauchy problem of parabolic type. Ann. Mat. Pura e Appl., IV, 33, 1983, 93-123. Zbl0524.47031MR725021DOI10.1007/BF01766013
  12. TOMARELLI, F., Regularity theorems and optimal error estimates for linear parabolic Cauchy problems. Numer. Math., 45, 1984, 23-50. Zbl0527.65036MR761880DOI10.1007/BF01379660

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.