Evolution governed by accretive mappings

Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 153)


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, fL 1 (I; X), u0X.


Strong Solution Mild Solution Lipschitz Constant Integral Solution Weak Derivative 
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© Birkhäuser Verlag Basel 2005

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