# On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes

Banach Center Publications (1992)

- Volume: 27, Issue: 1, page 23-44
- ISSN: 0137-6934

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topTon, Bui, and Łukaszewicz, Grzegorz. "On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes." Banach Center Publications 27.1 (1992): 23-44. <http://eudml.org/doc/262740>.

@article{Ton1992,

abstract = {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].},

author = {Ton, Bui, Łukaszewicz, Grzegorz},

journal = {Banach Center Publications},

keywords = {continuous extraction; existence; weak solution; non-stationary free boundary transmission problem; Navier-Stokes equations; nonlinear heat equation},

language = {eng},

number = {1},

pages = {23-44},

title = {On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes},

url = {http://eudml.org/doc/262740},

volume = {27},

year = {1992},

}

TY - JOUR

AU - Ton, Bui

AU - Łukaszewicz, Grzegorz

TI - On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes

JO - Banach Center Publications

PY - 1992

VL - 27

IS - 1

SP - 23

EP - 44

AB - 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].

LA - eng

KW - continuous extraction; existence; weak solution; non-stationary free boundary transmission problem; Navier-Stokes equations; nonlinear heat equation

UR - http://eudml.org/doc/262740

ER -

## References

top- [1] J. P. Aubin, Un théorème de compacité, C. R. Acad. Sci. Paris 256 (1963), 5042-5044.
- [2] E. Di Benedetto, Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl. (4) 130 (1982), 131-176.
- [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. Zbl0509.35067
- [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. Zbl0547.35117
- [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. Zbl0436.76056
- [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.
- [7] J.-F. Rodrigues, A steady-state Boussinesq-Stefan problem with continuous extraction, Ann. Mat. Pura Appl. 144 (1986), 203-218. Zbl0631.35083
- [8] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam 1977.

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