Report
Subsonic phase transition waves in bistable lattice models with small spinodal region
| العنوان: | Subsonic phase transition waves in bistable lattice models with small spinodal region |
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| المؤلفون: | Herrmann, Michael, Matthies, Karsten, Schwetlick, Hartmut, Zimmer, Johannes |
| المصدر: | SIAM J. Math. Anal., vol. 45, no.5, pp. 2625-2645, 2013 |
| سنة النشر: | 2012 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Dynamical Systems, 37K60, 47H10, 74J30, 82C26 |
| الوصف: | Phase transitions waves in atomic chains with double-well potential play a fundamental role in materials science, but very little is known about their mathematical properties. In particular, the only available results about waves with large amplitudes concern chains with piecewise-quadratic pair potential. In this paper we consider perturbations of a bi-quadratic potential and prove that the corresponding three-parameter family of waves persists as long as the perturbation is small and localised with respect to the strain variable. As a standard Lyapunov-Schmidt reduction cannot be used due to the presence of an essential spectrum, we characterise the perturbation of the wave as a fixed point of a nonlinear and nonlocal operator and show that this operator is contractive in a small ball in a suitable function space. Moreover, we derive a uniqueness result for phase transition waves with certain properties and discuss the kinetic relation. Comment: revised version with extended introduction, improved perturbation method, and novel uniqueness result; 20 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1137/120877878 |
| URL الوصول: | http://arxiv.org/abs/1206.0268 |
| رقم الانضمام: | edsarx.1206.0268 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1137/120877878 |
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