Abstract
Mean hyperbolic systems permit non-hyperbolic behavior at certain moments during the evolution process T(t,s), owing to non-fixed error hyperbolic degree ε(t,s). Despite the coexistence of compression and expansion behaviors in generalized stable and unstable subspaces, mean hyperbolic systems admit fixed average contraction and expansion rates measured at sufficiently long time. To discuss the relationship between admissibility and mean hyperbolicity for evolution equations, our main goal is to construct admissible function classes and invariant decomposition with generalized stable and unstable subspaces. As applications, the mean hyperbolicity of damped wave equations with variable coefficients and the roughness of mean hyperbolicity are presented.
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