Group actions on monotone skew-product semiflows with applications

  • Feng Cao

    Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China
  • Mats Gyllenberg

    University of Helsinki, Finland
  • Yi Wang

    University of Scinece and Technology of China, Hefei, Anhui, China


We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group -action has been considered on a strongly monotone skew-product semiflow. Here we relax the strong monotonicity and compactness requirements, and establish a theory concerning symmetry or monotonicity properties of uniformly stable 1-cover minimal sets. We then apply this theory to show rotational symmetry of certain stable entire solutions for a class of nonautonomous reaction-diffusion equations on , as well as monotonicity of stable traveling waves of some nonlinear diffusion equations in time-recurrent structures including almost periodicity and almost automorphy.

Cite this article

Feng Cao, Mats Gyllenberg, Yi Wang, Group actions on monotone skew-product semiflows with applications. J. Eur. Math. Soc. 18 (2016), no. 1, pp. 195–223

DOI 10.4171/JEMS/588