A study on asymptotic behavior of solutions for evolution equations

演化方程解的渐近行为研究

• 批准号: 14540208
• 负责人: IKEHATA Ryo
• 金额: $ 1.02万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540208/
• 关键词: Wave equation; exterior domain; Energy; decay; asymptotics of solutions; 外部問題; エネルギー減衰; 消散項; 非有界領域; 臨界指数; 減衰評価

We first discussed the possibility of applications of the device due to Ikehata-Matsuyama (which was newly developed in 1999) to some evolution equations in unbounded domains. For this we have obtained several results concerning the global well-posedness result of damped wave equations with the Fujita type power nonlinearity. And also by the device we have obtained the new result concerning the diffusion phenomenon of abstract second-order evolution equations.Second we have found the new decay estimates of (semilinear) damped wave equations, which are dealt with in the N-dimensional half space.Third, by the two methods due to Ikehata-Matsuyama above and Todorova-Yordanov we have succeeded in removing the compactness of the support on the initial data in order to obtain local energy decay estimates of the wave equation in an exterior domain with a star-shaped complement. This result completely generalizes that obtained by Morawetz in 1961. It should be pointed out that the method used to derive local enegy decay results has many wide applications to hyperbolic equations in exterior domains.

我们首先讨论了Ikehata-Matsuyama（1999年新发展的）的装置应用于无界区域上的某些发展方程的可能性。为此，我们得到了几个关于具有Fujita型幂非线性项的阻尼波方程的整体适定性结果。利用该装置我们得到了抽象二阶发展方程扩散现象的新结果。其次，我们得到了（半线性）阻尼波动方程，在N维半空间中进行处理。第三，通过两种方法，由于池田松山上述和托多罗娃-Yordanov，我们已经成功地消除了初始数据的支持的紧凑性，以获得当地的能量衰减估计的波动方程在外部域与星形补充。这个结果完全推广了Morawetz在1961年得到的结果。应该指出的是，这种导出局部能量衰减结果的方法对于外区域上的双曲型方程有着广泛的应用。

项目成果

Local energy decay for linear wave equations with non-compactly supported initial data

具有非紧支持初始数据的线性波动方程的局部能量衰减

• 发表时间: 2004
• 期刊: Math. Methods Appl. Sci. 27・16
• 作者: J.Sugie;N.Yamaoka;Norio Yoshida;R.Ikehata
• 通讯作者: R.Ikehata

Local energy decay for linear wave equations with variable coefficients

变系数线性波动方程的局部能量衰减

• 发表时间: 2005
• 期刊: J. Math. Anal. Appl. 306・1
• 作者: M.Kawashita;W.Kawashita;H.Soga;Makoto Masumoto;T.Morita;増本 誠;H.Matsunaga;R.Ikehata;Makoto Masumoto;M.Kawashita;Masakazu Shiba;N.Yamaoka;M.Kawashita;Takao Kato;H.Matsunaga;R.Ikehata
• 通讯作者: R.Ikehata

Decay estimates of solutions for dissipative wave equations in R^N with lower power nonlinearities

• DOI: 10.2969/jmsj/1191418635
• 发表时间: 2004-04
• 期刊: Journal of The Mathematical Society of Japan
• 影响因子: 0.7
• 作者: R. Ikehata;Yasuaki Miyaoka;T. Nakatake

Ryo IKEHATA: "New decay estimates for linear damped wave equations and its application to nonlinear problem"Math.Methods in the Appl.Sci.. In press.

Ryo IKEHATA：“线性阻尼波动方程的新衰减估计及其在非线性问题中的应用”《应用科学中的数学方法》正在出版。

Ryo IKEHATA: "Local energy decay for linear wave equations with non-compactly supported initial data"Math.Methods in the Appl.Sci.. In press.

Ryo IKEHATA：“具有非紧支持初始数据的线性波动方程的局部能量衰减”应用科学中的数学方法。正在出版。