Evolution governed by accretive mappings
Now we replace the weak compactness and monotonicity method by the norm topology technique and a completeness argument. Although, in comparison with the former technique, this method is not the basic one, it widens in a worthwhile way the range of the monotone-mapping approach presented in Chapter 8.
Again we consider the Cauchy problem (8.4) but now with A : dom(A) → X an m-accretive mapping (or, more generally, A + λI m-accretive for some λ ≥ 0), X a Banach space whose norm will be denoted by ‖ · ‖ as in Chap. 3, dom(A) dense in X, f ∈ L 1 (I; X), u0 ∈ X.
KeywordsStrong Solution Mild Solution Lipschitz Constant Integral Solution Weak Derivative
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