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July  2009, 23(3): 733-753. doi: 10.3934/dcds.2009.23.733

Differential equations in metric spaces with applications

Rinaldo M. Colombo 1, and  Graziano Guerra 2,

1. 

Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy
2. 

Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8 – 20126 Milano

Received  December 2007 Revised  February 2008 Published  November 2008

This paper proves the local well posedness of differential equations in metric spaces under assumptions that allow to comprise several different applications. We consider below a system of balance laws with a dissipative non local source, the Hille-Yosida Theorem, a generalization of a recent result on nonlinear operator splitting, an extension of Trotter formula for linear semigroups and the heat equation.
Keywords: Nonlinear differential equations in metric spaces; Balance laws; Stop problem; Operator Splitting.
Mathematics Subject Classification: Primary: 34G20, 47J35; Secondary: 35L65.
Citation: Rinaldo M. Colombo, Graziano Guerra. Differential equations in metric spaces with applications. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 733-753. doi: 10.3934/dcds.2009.23.733
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