Diffusive-dispersive travelling waves and kinetic relations. II A hyperbolic-elliptic model of phase-transition dynamics
Authors: Bedjaoui, Nabil; LeFloch, Philippe G.
Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 132, Number 3, 21 June 2002 , pp. 545-565(21)
Publisher: Royal Society of Edinburgh
Abstract:We deal here with a mixed (hyperbolic-elliptic) system of two conservation laws modelling phase-transition dynamics in solids undergoing phase transformations. These equations include nonlinear viscosity and capillarity terms. We establish general results concerning the existence, uniqueness and asymptotic properties of the corresponding travelling wave solutions. In particular, we determine their behaviour in the limits of dominant diffusion, dominant dispersion or asymptotically small or large shock strength. As the viscosity and capillarity parameters tend to zero, the travelling waves converge to propagating discontinuities, which are either classical shock waves or supersonic phase boundaries satisfying the Lax and Liu entropy criteria, or else are undercompressive subsonic phase boundaries. The latter are uniquely characterized by the so-called kinetic function, whose properties are investigated in detail here.
Document Type: Research Article
Publication date: June 21, 2002