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Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model

Francisco Guillén-González, Juan Vicente Gutiérrez-Santacreu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze two numerical schemes of Euler type in time and C0 finite-element type with 1 -approximation in space for solving a phase-field model of a binary alloy with thermal properties. This model is written as a highly non-linear parabolic system with three unknowns: phase-field, solute concentration and temperature, where the diffusion for the temperature and solute concentration may degenerate. The first scheme is nonlinear, unconditionally stable and convergent. The other scheme is linear...

Stability of a model for the Belousov-Zhabotinskij reaction

Vladimír Haluška (1989)

Aplikace matematiky

The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.

Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček (2001)

Mathematica Bohemica

Steady-state system of equations for incompressible, possibly non-Newtonean of the p -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain Ω n , n = 2 or 3, with heat sources allowed to have a natural L 1 -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if p > 3 / 2 (for n = 2 ) or if p > 9 / 5 (for n = 3 ).

Stefan problems with a concentrated capacity

Enrico Magenes (1998)

Bollettino dell'Unione Matematica Italiana

Vengono brevemente studiati i problemi di Stefan su «capacità concentrate»,seguendo l'approccio recentemente introdotto di G. Savaré e A. Visintin.

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