The energy method in the Fourier space is useful in deriving the decay estimates for problems in the whole space Rn. In this paper, we study half space problems in R+n=R+×Rn-1 and develop the energy method in the partial Fourier space obtained by taking the Fourier transform with respect to the tangential variable x'∈Rn-1. For the variable x1∈R+ in the normal direction, we use L2 space or weighted L2 space. We apply this energy method to the half space problem for damped wave equations with a nonlinear convection term and prove the asymptotic stability of planar stationary waves by showing a sharp convergence rate for t→∞. The result obtained in this paper is a refinement of the previous one in Ueda et al. (2008) .
All Science Journal Classification (ASJC) codes
- Applied Mathematics