On the nonrelativistic limit of a semilinear field equation in a uniform and isotropic space

Abstract

The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and global and blow-up solutions are shown in Sobolev spaces. The role of spatial variance on the problem is studied,and some dissipative properties of the limit-equation are remarked.