Abstract
We study the Cauchy problem for a 2 × 2-system of conservation laws: v t − u x = 0, u t − σ(v) t = 0 which describe the phase transition. Two constant states satisfying the Maxwell equal-area principle constitute an admissible stationary solution; a small perturbation of these Maxwell states will be our initial data. We shall show that: there exists a global in time propa gating phase boundary which is admissible in the sense that it satisfies the Abeyaratne-Knowles kinetic condition; the states outside the phase boundary tend to the Maxwell states as time goes to infinity.
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Asakura, F. (1999). Large Time Stability of Propagating Phase Boundaries. In: Fey, M., Jeltsch, R. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 129. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8720-5_3
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DOI: https://doi.org/10.1007/978-3-0348-8720-5_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9742-6
Online ISBN: 978-3-0348-8720-5
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