Differential and Integral Equations

A vanishing viscosity fluidized bed model

Gonzalo Galiano, Julián Velasco, and Santiago de Vicente

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The evolution of one-dimensional fluidized beds may be modeled in form of a system of partial differential equations of the compressible Navier-Stokes type where the viscosity depends on the density, which may vanish, the source term is nonlinear, and the constitutive law for the pressure blows up for finite values of the density. A finite-differences scheme is used to solve an approximated problem in Lagrangian coordinates, which we show to be equivalent to the corresponding problem in Eulerian coordinates. We then prove compactness and convergence properties of the sequence of solutions of the approximated problems and partially identify the limit as a solution of the original problem.

Article information

Differential Integral Equations, Volume 16, Number 4 (2003), 473-498.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76T10: Liquid-gas two-phase flows, bubbly flows


Galiano, Gonzalo; Velasco, Julián; de Vicente, Santiago. A vanishing viscosity fluidized bed model. Differential Integral Equations 16 (2003), no. 4, 473--498. https://projecteuclid.org/euclid.die/1356060654

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