LAUSR

Abstract In this article, we study an initial-boundary-value problem of the sixth order Boussinesq equation on a half line with nonhomogeneous boundary conditions: { u t t − u x x + β u x x x x − u x x x x x x + ( u 2 ) x x = 0 , x > 0 ,  t > 0 , u ( x , 0 ) = φ ( x ) , u t ( x , 0 ) = ψ ″ ( x ) , x > 0 , u ( 0 , t ) = h 1 ( t ) , u x x ( 0 , t ) = h 2 ( t ) , u x x x x ( 0 , t ) = h 3 ( t ) , t > 0 , where β = ± 1 . It is shown that the problem is locally well-posed in C ( R l o c + , H s ( R + ) ) with initial condition ( φ , ψ ) ∈ H s ( R + ) × H s − 1 ( R + ) and boundary condition ( h 1 , h 2 , h 3 ) in the product space H s + 1 3 ( R + ) × H s − 1 3 ( R + ) × H s − 3 3 ( R + ) for − 1 2 s ≤ 0 .