Group actions on monotone skew-product semiflows with applications

Cao, Feng, Gyllenberg, Mats, and Wang, Yi. "Group actions on monotone skew-product semiflows with applications." Journal of the European Mathematical Society 018.1 (2016): 195-223. <http://eudml.org/doc/277381>.

@article{Cao2016,
abstract = {We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-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 $\mathbb \{R\}^n$, as well as monotonicity of stable traveling waves of some nonlinear diffusion equations in time-recurrent structures including almost periodicity and almost automorphy.},
author = {Cao, Feng, Gyllenberg, Mats, Wang, Yi},
journal = {Journal of the European Mathematical Society},
keywords = {monotone skew-product semiflows; group actions; rotational symmetry; reaction-diffusion equations; traveling waves; monotone skew-product semiflows; group actions; rotational symmetry; reaction-diffusion equations; traveling waves},
language = {eng},
number = {1},
pages = {195-223},
publisher = {European Mathematical Society Publishing House},
title = {Group actions on monotone skew-product semiflows with applications},
url = {http://eudml.org/doc/277381},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Cao, Feng
AU - Gyllenberg, Mats
AU - Wang, Yi
TI - Group actions on monotone skew-product semiflows with applications
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 1
SP - 195
EP - 223
AB - We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-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 $\mathbb {R}^n$, as well as monotonicity of stable traveling waves of some nonlinear diffusion equations in time-recurrent structures including almost periodicity and almost automorphy.
LA - eng
KW - monotone skew-product semiflows; group actions; rotational symmetry; reaction-diffusion equations; traveling waves; monotone skew-product semiflows; group actions; rotational symmetry; reaction-diffusion equations; traveling waves
UR - http://eudml.org/doc/277381
ER -