On initial-boundary value problems for one-dimension semilinear wave equations with null conditions

Abstract

We consider the initial-boundary value problem on R+×R+ for one-dimension systems of semilinear wave equations with null conditions. We show that for homogeneous Dirichlet or Neumann boundary values and sufficiently small initial data, classical solutions always globally exist. Furthermore, we also prove that the global solution is asymptotically free in the energy sense.