Stability of C~0 semigroups which possess global attractors

摘要

Let Sg(M) be a set of all the continuous semigroups in a Banach space M, endowed with C~0 topology. X represents all the C~0 semigroups which possess global attractors in M. A C~0 semigroup {s(t))_t ≥ 0 ∈ χ is called stable, if there is a C~0 ε-neighbourhood U of {S(t)}_t ≥ 0, such that U is contained in χ. Using the measure of noncompactness, we prove that the continuous semigroup which possesses the global attractor is in general not stable.