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
Colombo, R., Guerra, G. (2009). Differential equations in metric spaces with applications. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 23(3), 733-753 [10.3934/dcds.2009.23.733].
Differential equations in metric spaces with applications
GUERRA, GRAZIANO
2009
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
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