Differential Equations in Metric Spaces with Applications

TL;DR

This paper establishes the local well-posedness of differential equations in metric spaces, encompassing various applications such as balance laws, semigroup theory, and heat equations, under broad assumptions.

Contribution

It introduces a unified framework for analyzing differential equations in metric spaces, extending existing results to new classes of problems and applications.

Findings

Proves local well-posedness for a broad class of differential equations in metric spaces.

Extends the Hille-Yosida Theorem to new contexts.

Generalizes nonlinear operator splitting and Trotter formula for linear semigroups.

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.