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Stationary solutions to the Falk system on shape memory alloys

✍ Scribed by Takashi Suzuki; Souhei Tasaki

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
266 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We study the Falk model system describing martensitic phase transitions in shape memory alloys. Its physically closed stationary state is formulated as a nonlinear eigenvalue problem with a non‐local term. Then, some results on existence, stability, and bifurcation of the solution are proven. In particular, we prove the existence of dynamically stable nontrivial stationary solutions. Copyright Β© 2009 John Wiley & Sons, Ltd.

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## Abstract In this article a stability result for the Falk model system is proven. The Falk model system describes the martensitic phase transitions in shape memory alloys. In our setting, the steady state is a nonlocal elliptic problem. We show the dynamical stability for the linearized stable cr