半直线上修正Kawahara方程的初边值问题

陶双平;陆善镇;

数学学报 ›› 2007, Vol. 50 ›› Issue (2) : 241-254.

PDF(526 KB)
PDF(526 KB)
数学学报 ›› 2007, Vol. 50 ›› Issue (2) : 241-254. DOI: 10.12386/A2007sxxb0029
论文

半直线上修正Kawahara方程的初边值问题

    陶双平;陆善镇;
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The Initial-Boundary Value Problem for the Modified Kawahara Equation on the Half Line

    Shuan Ping(1); TAO Shan Zhen L
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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.

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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初边值问题 / 存在性 / 修正Kawahara方程

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陶双平;陆善镇;. 半直线上修正Kawahara方程的初边值问题. 数学学报, 2007, 50(2): 241-254 https://doi.org/10.12386/A2007sxxb0029
Shuan Ping(1); TAO Shan Zhen L. The Initial-Boundary Value Problem for the Modified Kawahara Equation on the Half Line. Acta Mathematica Sinica, Chinese Series, 2007, 50(2): 241-254 https://doi.org/10.12386/A2007sxxb0029
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