A contribution to the theory of domain wall mass at high velocities

Two first integrals are given for the differential equations determining homogeneous motion of one-dimensional walls. These lead to a proof that such walls do not exist above the same critical velocity at which the Schlömann particular solution breaks down. It is speculated that this implies a high-mass solution even in one dimension, which would make the critical velocity an upper bound to any possible velocity in three dimensions, even though the numerical integration tried so far led only to masses which are smaller than in the Schlömann particular solution.