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The Cauchy Problem in Banach Spaces

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Nonlinear Differential Equations of Monotone Types in Banach Spaces

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Abstract

This chapter is devoted to the Cauchy problem associated with nonlinear quasi-accretive operators in Banach spaces. The main result is concerned with the convergence of the finite difference scheme associated with the Cauchy problem in general Banach spaces and in particular to the celebrated Crandall-Liggett exponential formula for autonomous equations, from which practically all existence results for the nonlinear accretive Cauchy problem follow in a more or less straightforward way.

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Authors and Affiliations

  1. Fac. Mathematics, Al. I. Cuza University, Blvd. Carol I 11, 700506, Iasi, Romania

    Viorel Barbu

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  1. Viorel Barbu
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Barbu, V. (2011). The Cauchy Problem in Banach Spaces. In: Nonlinear Differential Equations of Monotone Types in Banach Spaces. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5542-5_4

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