Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Mitsuhiro Nakao

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Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

机译：非线性局部耗散项在外部域中的非线性广义Klein-Gordon方程的能量衰减

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摘要

We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like ∣μ∣~αu, α > 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.

机译：我们导出了能量衰减估计，用于求解具有非线性局部耗散的外部域中的半线性波动方程的初边值问题。我们的方程包含一个吸收项，例如∣μ∣〜αu，α> 0，并且至少在α接近于0的情况下，可以视为广义Klein-Gordon方程。这一发现在我们的论点中起着至关重要的作用。

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来源
《Journal of the Mathematical Society of Japan》 |2012年第3期|p.851-883|共33页
作者
Mitsuhiro Nakao;
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作者单位

Faculty of Mathematics Kyushu University Moto-oka 744 Fukuoka 819-0398, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
energy decay; nonlinear wave equation; localized dissipation;

机译：能量衰减非线性波动方程局部耗散;

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专利

1. Energy decay to the Cauchy problem for a generalised nonlinear Klein-Gordon equation with a nonlinear dissipative term [J] . Mitsuhiro Nakao International journal of dynamical systems and differential equations . 2011,第3期

机译：具有非线性耗散项的广义非线性Klein-Gordon方程的Cauchy问题能量衰减
2. Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity [J] . Nakao M. Journal of Differential Equations . 2013,第11期

机译：具有非线性局部耗散和导数非线性的Klein-Gordon方程外部问题的整体衰减解的存在
3. Remarks on the energy decay for nonlinear wave equations with nonlinear localized dissipative terms [J] . Nakao M. Nonlinear Analysis: An International Multidisciplinary Journal . 2010,第7期

机译：关于带有非线性局部耗散项的非线性波动方程的能量衰减的说明
4. On the solutions for nonlinear wave equations with localized dissipations in exterior domains [C] . Makoto Nakamura MSJ-SI International Conference "Nonlinear Dynamics in Partial Differential Equations" . 2015

机译：关于外部域局部耗散的非线性波动方程解
5. On the Laplacian and fractional Laplacian in exterior domains, and applications to the dissipative quasi-geostrophic equation. [D] . Kosloff, Leonardo. 2012

机译：关于外部域中的拉普拉斯算子和分数阶拉普拉斯算子，及其在耗散拟地转方程中的应用。
6. Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations [O] . Kamruzzaman Khan, M Ali Akbar, S M Rayhanul Islam -1

机译：（1 + 1）维非线性色散修正的Benjamin-Bona-Mahony方程和Klein-Gordon耦合方程的精确解
7. Existence of Global Decaying Solutions to the Cauchy Problem for a Nonlinear Dissipative Wave Equation of Klein-Gordon Type with a Derivative Nonlinearity [O] . Mitsuhiro Nakao 2012

机译：具有衍生非线性的克莱因 - 戈登型非线性耗散波动方程的全局衰减解决方案存在
8. A generalized perturbation expansion for the klein-gordon equation with a small nonlinearity [R] . Montgomery, D. 1964

机译：具有小非线性的klein-gordon方程的广义摄动展开式

Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

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