Metastability for hyperbolic variations of Allen–Cahn equation


Por: Folino R.

Publicada: 1 ene 2018
Resumen:
The Allen–Cahn equation is a parabolic reaction–diffusion equation that has been originally proposed in Allen and Cahn (Acta Metall 27:1085–1095, 1979, [1]) to describe the motion of antiphase boundaries in iron alloys. In general, reaction–diffusion equations of parabolic type undergo the same criticisms of the linear diffusion equation, mainly concerning lack of inertia and infinite speed of propagation of disturbances. To avoid these unphysical properties, many authors proposed hyperbolic variations of the classic reaction–diffusion equations. Here, we consider a hyperbolic variation of the Allen–Cahn equation and present some results contained in Folino (J Hyperbolic Differ Equ 14:1–26, 2017, [6]) and Folino et al. (Metastable dynamics for hyperbolic variations of the Allen–Cahn equation, 2016, [8]) concerning the metastable dynamics of solutions. We study the singular limit of the solutions as the diffusion coefficient e ? 0+ and show that the hyperbolic version shares the well-known dynamical metastability valid for the parabolic equation. © Springer International Publishing AG, part of Springer Nature 2018.

Filiaciones:
Folino R.:
 Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Via Vetoio, L’Aquila, Coppito 67100, Italy
ISSN: 21941009
Editorial
Springer New York LLC, 233 SPRING STREET, NEW YORK, NY 10013, UNITED STATES, Estados Unidos America
Tipo de documento: Conference Paper
Volumen: 236 Número:
Páginas: 551-563