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Global solvability of the equations of one-dimensional nonisothermic motion of a two-phase mixture. II. Results on solvability

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Abstract

Using the vanishing viscosity method, the existence is proved of a weak solution for the problem of one-dimensional motion of a two interpenetrative viscous incompressible fluids on an arbitrary finite time interval.

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References

  1. A. A. Papin, “Global Solvability of the Equations of One-Dimensional NonisothermicMotion of a Two-Phase Mixture. I. Statement of the Problem and Auxiliary Assertions,” Sibirsk. Zh. Industr. Mat. 9(2(26)), 116–136 (2006) [J. Appl. Industr.Math. 2 (2), 231–251 (2008)].

    MathSciNet  Google Scholar 

  2. R. I. Nigmatulin, Dynamics of Multiphase Media, Vol. 1 (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  3. K. L. Rajagopal and L. Tao, Mechanics of Mixtures (World Sci., Singapore, 1995).

    MATH  Google Scholar 

  4. V. V. Pukhnachov, O. V. Voinov, A. G. Petrova, E. N. Zhuravleva, and O. A. Gudz, “Dynamics, Stability and Solidification of Emulsion Under the Action of Thermocapillary Forces and Microacceleration,” in Lecture Notes in Physics, Vol. 628: Interfacial Fluid Dynamics and Transport Processes, pp. 325–354 (Springer, Berlin, 2003).

    Google Scholar 

  5. S. K. Gard and J. W. Pritchett, “Dynamics of Gas-Fluidized Beds,” J. Appl. Physics 46(10), 4493–4500 (1975).

    Article  Google Scholar 

  6. V. V. Vedernikov and V. N. Nikolaevskii, “Mechanics Equations for Porous Media Saturated by a Two-Phase Liquid,” Izv. Akad. Nauk SSSR Mekh. Zhidk.Gaza, No. 5, 165–169 (1978) [Fluid Dyn. 13, 769–773 (1979)].

  7. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasi-Linear Equations of Parabolic Type (Nauka, Moscow, 1967; Amer.Math. Soc., Providence, RI, 1968).

    Google Scholar 

  8. S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids (Nauka, Novosibirsk, 1983; North-Holland, Amsterdam, 1990).

    Google Scholar 

  9. A. A. Papin, “Local Solvibility in Time of the System of One-Dimensional Motion of Two Interpenetrating Viscous Incompressible Liquids,” Dinamika Sploshn. Sredy 114, 64–70 (1999).

    MATH  MathSciNet  Google Scholar 

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Correspondence to A. A. Papin.

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Original Russian Text © A.A. Papin, 2006, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2006, Vol. IX, No. 3(27), pp. 111–123.

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Papin, A.A. Global solvability of the equations of one-dimensional nonisothermic motion of a two-phase mixture. II. Results on solvability. J. Appl. Ind. Math. 2, 367–378 (2008). https://doi.org/10.1134/S1990478908030071

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