| Abstract: |
| We discuss a general framework of monotone skew-product semiflows under a connected group action 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, as well as monotonicity of stable traveling waves of some nonlinear diffusion equations in time recurrent structures including almost periodicity and almost automorphy. |
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