论文标题
非线性波方程解的持久性和渐近分析
Persistence and asymptotic analysis of solutions of nonlinear wave equations
论文作者
论文摘要
我们考虑溶液在广义波方程中的持久性能，包括弹性杆和浅水模型的振动，例如BBM，DAI，Camassa-Holm和Dullin-Gottwald-Holm方程，以及一些最近具有Coriolis效应的浅水方程。我们建立了独特的延续结果，并为所考虑的通用类别的解决方案展示了渐近谱。从这些结果中，我们证明了对方程式的非平凡空间紧凑的解决方案的不存在。作为后果，我们根据通用阶层的结果研究了前面提到的方程式。
We consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the BBM, the Dai's, the Camassa-Holm, and the Dullin-Gottwald-Holm equations, as well as some recent shallow water equations with the Coriolis effect. We establish unique continuation results and exhibit asymptotic profiles for the solutions of the general class considered. From these results we prove the non-existence of non-trivial spatially compactly supported solutions for the equation. As an aftermath, we study the equations earlier mentioned in light of our results for the general class.
