Multidimensional stability of planar travelling waves

The multidimensional stability of planar travelling waves for systems of reaction-diffusion equations is considered in the case that the diffusion matrix is tile identity. It is shown that if the wave is exponentially orbitally stable in one space dimension, then it is stable for x is an element of R(n), n greater than or equal to 2. Furthermore, it is shown that the perturbation of the wave decays like t(-(n-1)/4) as t --> infinity. The result is proved via an application of linear semigroup theory.