Low Regularity Solution of the Initial-Boundary-Value Problem for the ＂Good＂ Boussinesq Equation on the Half Line

we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line
{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0.
u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）,
u（x,0）=f（x）,δtu（x,0）=δxh（x）.
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product space
H^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋）
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered.

Low regularity solution of the initial-boundary-value problem for the “good” Boussinesq equation on the half line

we study an initial-boundary-value problem for the “good” Boussinesq equation on the half line

$ \left\{ \begin{gathered} \partial _t^2 u - \partial _x^2 u + \partial _x^4 u + \partial _x^2 u^2 = 0, t > 0, x > 0, \hfill \\ u\left( {0,t} \right) = h_1 \left( t \right), \partial _x^2 u\left( {0,t} \right) = \partial _t h_2 \left( t \right), \hfill \\ u\left( {x,0} \right) = f\left( x \right), \partial _t u\left( {x,0} \right) = \partial _x h\left( x \right) \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} \partial _t^2 u - \partial _x^2 u + \partial _x^4 u + \partial _x^2 u^2 = 0, t > 0, x > 0, \hfill \\ u\left( {0,t} \right) = h_1 \left( t \right), \partial _x^2 u\left( {0,t} \right) = \partial _t h_2 \left( t \right), \hfill \\ u\left( {x,0} \right) = f\left( x \right), \partial _t u\left( {x,0} \right) = \partial _x h\left( x \right) \hfill \\ \end{gathered} \right.
Keywords:	Boussinesq equation  existence  initial-boundary-value problem
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