半直线上修正Kawahara方程的初边值问题

The Initial-Boundary Value Problem for the Modified Kawahara Equation on the Half Line

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．

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 Kawahara equation on the half line is locally solvable if the initial function belongs to H^s（Rx^＋） and the boundary .function belongs to H^（s＋2）/5（Rt^＋） with 1/4≤s〈2.