We consider the nonrelativistic limit of a semilinear field equation in a homogeneous and isotropic space, where the scale function of the space is constructed based on the Einstein equations. Furthermore, we examine the Cauchy problem for the limit equation and show the existence of global and blowup solutions in Sobolev spaces. Finally, we study the effects of spatial variance on the problem and remark on some dissipative and antidissipative properties of the limit equation.
"On the nonrelativistic limit of a semilinear field equation in a homogeneous and isotropic space." Kyoto J. Math. 60 (4) 1333 - 1359, December 2020. https://doi.org/10.1215/21562261-2019-0063