Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
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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.
Date issued
2022-01Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1432-0673
0003-9527