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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.

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Authors and Affiliations

  1. University of California, Los Angeles

    M. G. Crandall & A. Pazy

  2. The Hebrew University of Jerusalem, Jerusalem, Israel

    M. G. Crandall & A. Pazy

Authors
  1. M. G. Crandall
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  2. A. Pazy
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Additional information

Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462. and in part by the Office of Naval Research under Contract N000-14-69-A-0200-4022. Reproduction in whole or in part is permitted for any purpose of the United States Government.

This research was partially supported by the NSF Grant #GP-18127.

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Crandall, M.G., Pazy, A. Nonlinear evolution equations in Banach spaces. Israel J. Math. 11, 57–94 (1972). https://doi.org/10.1007/BF02761448

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  • DOI: https://doi.org/10.1007/BF02761448

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