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| 变系数的一般型发展方程的色散估计 | |
| 引用本文： | 王华,崔尚斌. 变系数的一般型发展方程的色散估计[J]. 数学进展, 2007, 36(4): 503-512 |
| 作者姓名： | 王华 崔尚斌 |
| 作者单位： | 中山大学数学系,广州,广东,510275 |
| 摘 要： | 本文研究的是带变系数的一般型线性发展方程.首先建立了其基本解的一系列色散估计:Kato光滑型估计,极大函数估计及Strichartz估计.最后应用这些估计研究了一些非自治非线性色散方程的初值问题在H~s(R)空间中的局部可解性. |
| 关 键 词： | 发展方程 色散估计 局部可解点 |
| 文章编号： | 1000-0917（2007）04-0503-10 |
| 修稿时间： | 2005-09-27 |
Dispersive Estimates for a General Class of Evolution Equations With Variable Coefficients |
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| WANG Hua,CUI Shangbin. Dispersive Estimates for a General Class of Evolution Equations With Variable Coefficients[J]. Advances in Mathematics(China), 2007, 36(4): 503-512 | |
| Authors: | WANG Hua CUI Shangbin |
| Affiliation: | Institute of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong, 510275, P. R. China |
| Abstract: | In this paper we establish a series of dispersive estimates for the fundamental solution of a general class of linear evolution equations with variable coefficients.These estimates include the Kato smoothing effect estimate,the maximal function estimate,and the Strichartz estimates.As an application of these estimates we use them to study local solvability of the initial value problem of some non-autonomous nonlinear dispersive equations in the Sobolev spaces H~s (R). |
| Keywords: | evolution equation dispersive estimates local solvability |
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