On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes
Ton, Bui ; Łukaszewicz, Grzegorz
Banach Center Publications, Tome 27 (1992), p. 23-44 / Harvested from The Polish Digital Mathematics Library
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The existence of a weak solution of a non-stationary free boundary transmission problem arising in the production of industrial materials is established. The process is governed by a coupled system involving the Navier--Stokes equations and a non-linear heat equation. The stationary case was studied in [7].

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:262740 
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     title = {On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes},
     journal = {Banach Center Publications},
     volume = {27},
     year = {1992},
     pages = {23-44},
     zbl = {0785.35114},
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Ton, Bui; Łukaszewicz, Grzegorz. On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes. Banach Center Publications, Tome 27 (1992) pp. 23-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z1p23bwm/

[000] [1] J. P. Aubin, Un théorème de compacité, C. R. Acad. Sci. Paris 256 (1963), 5042-5044.

[001] [2] E. Di Benedetto, Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl. (4) 130 (1982), 131-176.

[002] [3] A. Caffarelli, R. Kohn and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (6) (1982), 771-831. | Zbl 0509.35067

[003] [4] J. R. Cannon, E. Di Benedetto and G. H. Knightly, The bidimensional Stefan problem with convection: the time dependent case, Comm. Partial Differential Equations 8 (14) (1983), 1549-1604. | Zbl 0547.35117

[004] [5] J. R. Cannon, E. Di Benedetto and G. H. Knightly, The steady state Stefan problem with convection, Arch. Rational Mech. Anal. 73 (1980), 79-97. | Zbl 0436.76056

[005] [6] A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Transl. Math. Monographs 23, Providence, R.I., 1968.

[006] [7] J.-F. Rodrigues, A steady-state Boussinesq-Stefan problem with continuous extraction, Ann. Mat. Pura Appl. 144 (1986), 203-218. | Zbl 0631.35083

[007] [8] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam 1977.