๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Existence of global-in-time weak solutions to a modified Gilbert equation

โœ Scribed by P. Podio-Guidugli; V. Valente

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
374 KB
Volume
47
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

โœฆ Synopsis

We propose and study a modified form of the Gilbert equation for the evolution of the magnetization vector in a rigid ferromagnet. This modification, which we justify from the continuum-mechanical point of view, consists in the addition of a higher-order term, moduled by a small parameter. For each fixed value of the parameter, we prove existence of global-in-time weak solutions. We also prove that the solutions of the modified equation tend to the solutions of the Gilbert equation when the parameter tends to null.

๐Ÿ“œ SIMILAR VOLUMES

Existence of solutions to a global eikon
Existence of solutions to a global eikonal equation
โœ C. Nour ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 350 KB

We derive a geometric necessary and sufficient condition for the existence of solutions to a global eikonal equation. We also study the existence of a minimal solution to this equation, and its relation with the wellknown minimal time function.