| NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION |
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| 引用本文： | 王维克.NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION[J].数学物理学报(B辑英文版),2010(6):2051-2063. |
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| 作者姓名： | 王维克 |
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| 基金项目： | The authors are supported by National Science Foundation of China （11071162） and Shanghai Municipal Natural Science Foundation （09ZR1413500）. |
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| 摘 要： | In this paper, we will introduce how to apply Green’s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen’s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green’s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.
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| 关 键 词： | 非线性演化方程 演化系统 Stokes方程 格林函数方法 逐点估计 耗散结构 微局部分析 线性化系统 |
NONLINEAR EVOLUTION SYSTEMS AND GREEN'S FUNCTION |
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| Wang Weike.NONLINEAR EVOLUTION SYSTEMS AND GREEN'S FUNCTION[J].Acta Mathematica Scientia,2010(6):2051-2063. |
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| Authors: | Wang Weike |
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| Institution: | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
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| Abstract: | conservation laws with dissipative structure pointwise estimate Green＇s function generalized Huygen＇s principle |
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| Keywords: | conservation laws with dissipative structure pointwise estimate Green＇s function generalized Huygen＇s principle |
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