✦ LIBER ✦

Weak solutions for the Falk model system of shape memory alloys in energy class

✍ Scribed by Shuji Yoshikawa

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 168 KB
Volume: 28
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.621

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✦ Synopsis

Abstract

We show the unique global existence of energy class solutions for the Falk model system of shape memory alloys under the general non‐linearity as well as considered in Aiki (Math. Meth. Appl. Sci. 2000; 23: 299). Our main tools of the proofs are the Strichartz type estimate for the Boussinesq type equation and the maximal regularity estimate for the heat equation. Copyright © 2005 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Weak solutions for Falk's model of shape

Weak solutions for Falk's model of shape memory alloys

✍ Toyohiko Aiki 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 154 KB

In this paper we discuss the system of two partial di!erential equations governing the dynamics of phase transitions in shape memory alloys. We consider the one-dimensional model proposed by Falk, in which a term containing a fourth-derivative appears. The main purpose is to show the uniqueness for

Stability of the steady state for the Fa

Stability of the steady state for the Falk model system of shape memory alloys

✍ Takashi Suzuki; Shuji Yoshikawa 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 143 KB

## 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