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| A method is proposed to prove the global attractor existence for multivalued semiflows in Banach spaces with weak continuity properties. We introduce the condition (NW), "norm-to-weak", that generalizes to the multivalued case the norm-to-weak continuity property introduced earlier for semigroups. Equivalently, the condition states that the multivalued semiflow has weakly compact values and is strong-weak upper semicontinuous, and is weaker then the classical upper semicontinuity property used in the proof of the existence of the global attractor. Condition (NW) is natural to check e.g. for problems governed by differential inclusions where the multivalued term has the form of Clarke subdifferential. |
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