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1998-1999 | 25 | 2 | 179-220
Tytuł artykułu

Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.
Rocznik
Tom
25
Numer
2
Strony
179-220
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-01
Twórcy
  • Institute of Mathematics and Operations Research, Military University of Technology, S. Kaliskiego 2, 01-489 Warszawa, Poland
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
  • [1] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1986 (in Russian).
  • [2] B. Ducomet, Hydrodynamical models od gaseous stars, Rep. Math. Phys., to appear.
  • [3] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian); English transl.: Fluid Mechanics, Pergamon Press, Oxford, 1987.
  • [4] P. Secchi, On the motion of gaseous stars in presence of radiation, Comm. Partial Differential Equations 15 (1990), 185-204.
  • [5] V. A. Solonnikov, On boundary value problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian); English transl.: Proc. Steklov Inst. Math. 83 (1967).
  • [6] G. Ströhmer and W. M. Zajączkowski, Local existence of solutions of free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids, to appear.
  • [7] E. Zadrzyńska and W. M. Zajączkowski, On local motion of a general compressible viscous heat conducting fluid bounded by a free surface, Ann. Polon. Math. 59 (1994), 133-170.
  • [8] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat-conducting fluids, Bull. Polish Acad. Sci. Tech. Sci. 42 (1994), 197-207.
  • [9] E. Zadrzyńska and W. M. Zajączkowski, On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface, Ann. Polon. Math. 61 (1995), 141-188.
  • [10] E. Zadrzyńska and W. M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid, ibid. 63 (1996), 199-221.
  • [11] E. Zadrzyńska and W. M. Zajączkowski, On global motion of a compressible viscous heat conducting fluid bounded by a free surface, Acta Appl. Math. 37 (1994), 221-231.
  • [12] E. Zadrzyńska and W. M. Zajączkowski, On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary, in preparation.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-zmv25i2p179bwm
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