| 半直线上修正Kawahara方程的初边值问题 |
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| 引用本文： | 陶双平,陆善镇.半直线上修正Kawahara方程的初边值问题[J].数学学报,2007,50(2):241-254. |
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| 作者姓名： | 陶双平 陆善镇 |
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| 作者单位： | 西北师范大学数学与信息科学学院，北京师范大学数学科学学院 兰州 730070，北京 100875 |
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| 基金项目： | 国家自然科学基金(10571014) |
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| 摘 要： | 本文研究了半直线上修正Kawahara方程初边值问题的局部可解性．通过对相应强迫初值问题建立有关Duhamel强迫项的Strichartz型估计,证明了当初值函数φ(x)∈H~8(R_x~+),边值函数f(t)∈H~(s+2/5)(R_t~+)且1/4■s＜2时,半直线上修正Kawahara方程的初边值问题存在局部解．
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| 关 键 词： | 修正Kawahara方程 初边值问题 存在性 |
| 文章编号： | 0583-1431（2007）02-0241-14 |
| 收稿时间： | 2004-8-26 |
| 修稿时间： | 2004-08-28 |
The Initial-Boundary Value Problem for the Modified Kawahara Equation on the Half Line |
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| Shuang Ping TAO, Zhen LU.The Initial-Boundary Value Problem for the Modified Kawahara Equation on the Half Line[J].Acta Mathematica Sinica,2007,50(2):241-254. |
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| Authors: | Shuang Ping TAO Zhen LU |
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| Institution: | 1, College of Mathematics and Information Science, Northwest Normal University Lanzhou 730070, P. R. China ;2,School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | In this paper we study the local solvability of the initial-boundary problem for the modified Kawahara equation on the half line.By setting up some Strichartz-type estimates of the Duhamel forcing terms for a corresponding forced initial value problem, we prove that the initial-boundary problem of the modified Kawahaxa equation on the half line is locally solvable if the initial function belongs to H~8 (R_x~+) and the boundary function belongs to g~(x+2/5)(R_t~+) with 1/4■s＜2. |
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| Keywords: | modified Kawahara equation initial-boundary problem existence |
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