Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
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205_2021_1730_ReferencePDF.pdf
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3 MB
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Unknown
Checksum (MD5)
55b2f8de2410da5a650976c377b05aeb
Author(s)
Shao, Chengyang
Date Issued
January 2022
Journal
Archive for Rational Mechanics and Analysis
Publisher
Springer Berlin Heidelberg
Citation
Shao, Chengyang. 2022. "Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes."
Version
Author's final manuscript
Abstract
Abstract
The paper studies the long time behavior of a simplified model of an elastic membrane driven by surface tension and inner air pressure. The system is a degenerate quasilinear hyperbolic one that involves the mean curvature, and also includes a damping term that models the dissipative nature of genuine physical systems. With the presence of damping, a small perturbation of the sphere converges exponentially in time to the sphere, and without the damping the evolution that is
$$\varepsilon $$
ε
-close to the sphere has a life span longer than
$$\varepsilon ^{-1/6}$$
ε
-
1
/
6
. Both results are proved using a new Nash–Moser–Hörmander type theorem proved by Baldi and Haus.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00205-021-01730-8
