The Cauchy Problem in Banach Spaces

  • Viorel BarbuEmail author
Part of the Springer Monographs in Mathematics book series (SMM)


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.


Hilbert Space Banach Space Cauchy Problem Strong Solution Mild Solution 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fac. MathematicsAl. I. Cuza UniversityIasiRomania

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