具有任意增长非线性的紧凑流形上波方程的存在性和渐近稳定性

IF 1.3 2区 数学 Q1 MATHEMATICS
Marcelo M. Cavalcanti , Valéria N. Domingos Cavalcanti , José Guilherme Simion Antunes
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引用次数: 0

摘要

我们研究了无边界二维紧凑黎曼流形中任意增长的非线性和局部分布非线性耗散的波方程解的好求性、稳定化和炸毁问题。与以往文献不同的是,我们给出了一个不同的证明,它基于对原始问题的截断和对极限的穿越,从而一次获得能量特性和可观测性不等式,它们是获得能量均匀衰减率的基本要素。即使在亚临界、临界或超临界增长的情况下,我们证明的一个优点是衰减率与非线性无关。我们还可以处理能量小于基态(即山口定理的水平)的解的聚焦情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Existence and asymptotic stability for the wave equation on compact manifolds with nonlinearities of arbitrary growth

We study the wellposedness, stabilization and blow up of solutions of the wave equation with nonlinearities of arbitrary growth and locally distributed nonlinear dissipation posed in a 2-dimensional compact Riemannian manifold (M,g) without boundary. Differently of the previous literature we give a different proof based on the truncation of the original problem and passage to the limit in order to obtain in one shot, the energy identity as well as the Observability Inequality, which are the essential ingredients to obtain uniform decay rates of the energy. One advantage of our proof, even in the case of subcritical, critical or super critical growth, is that the decay rate is independent of the nonlinearity. We can also treat the focusing case for those solutions with energy less than d of the ground state, where d is the level of the Mountain Pass Theorem.

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来源期刊
CiteScore
3.30
自引率
0.00%
发文量
265
审稿时长
60 days
期刊介绍: Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
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