Differential equations in metric spaces with applications

Rinaldo M. Colombo; Graziano Guerra

doi:10.3934/dcds.2009.23.733

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2009, Volume 23, Issue 3: 733-753. Doi: 10.3934/dcds.2009.23.733

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Differential equations in metric spaces with applications

Rinaldo M. Colombo^1, and
Graziano Guerra^2,

1.
Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia
2.
Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8 – 20126 Milano

Received: November 30, 2007

Revised: January 31, 2008

Published: August 2009

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Abstract

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.

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