Vol.5 , No. 4, Publication Date: Dec. 24, 2018, Page: 95-100

[1] | Sherzod Imomnazarov, Mathematics Department, Novosibirsk University, Novosibirsk, Russia. |

[2] | Kholmatjon Imomnazarov, Mathematical Geophysics Department, Mathematics and Mathematical Geophysics Institute, Novosibirsk, Russia. |

[3] | Abdulkhamid Kholmurodov, Physics and Mathematics Department, Karshi State University, Karshi, Uzbekistan. |

[4] | Nasrutdin Dilmuradov, Physics and Mathematics Department, Karshi State University, Karshi, Uzbekistan. |

[5] | Musajon Mamatkulov, Mechanics and Mathematics Department, National University of Uzbekistan, Tashkent, Uzbekistan. |

A nonlinear system of equations describing the dynamics of the motion of two-phase fluids is considered. An initial-boundary value problem for the systems of viscous two-fluid media with phase equilibrium with respect to pressure whose solution or some integral characteristic of this solution becomes infinite in a finite time (blow-up) is investigated. Using the method of test functions proposed by Pokhozhaev and Mitidieri, the influence of boundary and initial conditions on the appearance, time and rate of destruction of solutions to these problems is examined. The theorem on the blow-up of the solution to the initial-boundary value problem is proved. The lifetime of the solution is estimated.

Keywords

Two-Speed Hydrodynamics, Mineralization, Porous Medium, Initial-Boundary Value Problem, Destruction in a Finite Time, Blow-Up

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