论文标题
准双曲系统建模弹性膜的长时间行为
Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
论文作者
论文摘要
该论文研究了一个系统的长时间行为，该系统描述了由表面张力和内部气压驱动的一块弹性膜的运动。该系统是一个涉及平均曲率的简并甲状腺双曲线，还包括一个阻尼术语，该术语模拟了真正物理系统的耗散性质。随着阻尼的存在，球体的小扰动会及时地呈指数收敛，而无需阻尼$ \ varepsilon $ -close到球体的演变，其寿命超过$ \ varepsilon^{ - 1/6} $。两种结果均使用Baldi和Haus证明的新的Nash-Moser-Hörmander型定理证明。
The paper studies the long time behavior of a system that describes the motion of a piece of 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 $\varepsilon$-close to the sphere has life span longer than $\varepsilon^{-1/6}$. Both results are proved using a new Nash-Moser-Hörmander type theorem proved by Baldi and Haus.
