Nonlinear evolution equations in Banach spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1972 English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 11, pages 57-94 (issn: 0021-2172, eissn: 1565-8511,

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Authors: Crandall, M. G.; Pazy, A.;

doi: 10.1007/bf02761448

Nonlinear evolution equations in Banach spaces

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Abstract

The evolution problem 0∈du/dt+A(t)u(t),u(s)=x, where theA(t) are nonlinear operators acting in a Banach space, is studied. Evolution operators are constructed from theA(t) under various assumptions. Basic properties of these evolution operators are established and their relationship to the evolution equation is determined. The results obtained extend several known existence theorems and provide generalized solutions of the evolution equation in more general cases.

Related Organizations

University of California, Los Angeles
United States
Hebrew University of Jerusalem
Israel

Keywords

Parabolic equations and parabolic systems, Differential equations in abstract spaces

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