Displaying similar documents to “Hamiltonian principle in the binary mixtures of Euler fluids with applications to the second sound phenomena”

Collisions and fractures: a model in S ⁢ B ⁢ D

Elena Bonetti, Michel Frémond (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We investigate collisions (assumed to be instantaneous) and fractures of three-dimensional solids. Equations of motion and constitutive laws provide a set of partial differential equations, whose corresponding variational problem may be solved in the space of special functions with bounded deformations ( S ⁢ B ⁢ D ), exploiting the direct method of calculus of variations.

The Hamilton Principle for Fluid Binary Mixtures with two Temperatures

Henri Gouin, Tommaso Ruggeri (2009)

Bollettino dell'Unione Matematica Italiana

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For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the total heat exchange between components. In this nonconservative case, a Gibbs dynamical identity connecting the equations of momenta, masses, energy and heat exchange allows to deduce the balance equation of energy of the mixture. Due to the unknown...

Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling ν ( p , · ) → + ∞ as p → + ∞

M. Bulíček, Josef Málek, Kumbakonam R. Rajagopal (2009)

Czechoslovak Mathematical Journal

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Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class...

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part I: Modelling of incompressible charged porous media

Kamyar Malakpoor, Enrique F. Kaasschieter, Jacques M. Huyghe (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory in which a deformable and charged porous medium is saturated with a fluid with dissolved ions. Four components are defined: solid, liquid, cations and anions. The aim of this paper is the construction of the Lagrangian model of the four-component system. It is shown that, with the choice of Lagrangian description of the solid skeleton, the motion of the other components can be described...