Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Counting the set of equilibria for a one-dimensional full model for phase transitions with microscopic movements

Authors: Jie Jiang and Yanyan Zhang
Journal: Quart. Appl. Math. 70 (2012), 665-683
MSC (2000): Primary 34B08, 35B40; Secondary 35K45, 80A22
DOI: https://doi.org/10.1090/S0033-569X-2012-01257-3
Published electronically: June 21, 2012
MathSciNet review: 3052084
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the steady states of a one-dimensional strongly nonlinear PDE system arising from the study of phase transitions with microscopic movements. Using the plane analysis method, we prove that the number of equilibria is at most infinitely countable. Furthermore, we show that the global solution to the evolution system converges to an equilibrium in $ H^3\times H^1$ as $ t\rightarrow +\infty $.

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Additional Information

Jie Jiang
Affiliation: Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, People’s Republic of China
Email: jiangbryan@gmail.com

Yanyan Zhang
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
Email: yanyanzhangfd@yahoo.cn

DOI: https://doi.org/10.1090/S0033-569X-2012-01257-3
Keywords: Phase transitions, microscopic movements, steady states, convergence to equilibrium
Received by editor(s): October 23, 2010
Published electronically: June 21, 2012
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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