The Cauchy problem for the semilinear diffusion equation is considered in the de Sitter spacetime with the spatial zero-curvature. Global solutions and their asymptotic behaviors for small initial data are obtained for positive and negative Hubble constants. The effects of the spatial expansion and contraction are studied on the problem.
"Remarks on global solutions for the semilinear diffusion equation in the de Sitter spacetime." Hokkaido Math. J. 49 (3) 481 - 508, October 2020. https://doi.org/10.14492/hokmj/1607936539