A NON-HOMOGENEOUS BOUNDARY VALUE PROBLEM OF THE SIXTH ORDER BOUSSINESQ EQUATION IN A QUARTER PLANE

摘要

The paper is concerned with an initial-boundary-value problem of the sixth order Boussinesq equation posed on a quarter plane with non-homogeneous boundary conditions:(U-tt - U-xx + beta u(xxxx) - u(xxxxxx) + (u(2))(xx) =0, for x > 0, t > 0, u(x, 0) = phi(x), u(t)(x, 0) = psi(x), (1) u(0, t) = h(1)(t), u(xx)(0, t) = h(2)(t), u(xxxx)(0, t) = h(3)(t),where beta = +/- 1. It is shown that the problem is locally well-posed in the space H-s(R+) for any 0 <= s < 13/2 with the initial data (phi, psi) in the spaceH-S(R+) x Hs-1 (R+)and the naturally compatible boundary datah(1)is an element of H-loc(s+1/3) (R+), h(2) is an element of H-loc(s-1/3) (R+) and h(3) is an element of H-loc(s-3/3) (R+)with optimal regularity.