Exotic n-d'Alembert PDE's and Stability

TL;DR

This paper explores exotic n-d'Alembert PDEs within algebraic topology, demonstrating their unique properties, existence, and stability, especially when Cauchy manifolds are exotic spheres or have boundaries that are exotic spheres.

Contribution

It introduces and analyzes exotic n-d'Alembert PDEs with Cauchy manifolds related to exotic spheres, providing new existence and stability results.

Findings

Existence theorems for exotic n-d'Alembert PDEs

Global stability results for these PDEs

Characterization of Cauchy manifolds as exotic spheres

Abstract

In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, {\em exotic $n$-d'Alembert PDE's} are considered. These are $n$-d'Alembert PDE's, $(d'A)_n$, admitting Cauchy manifolds $N\subset (d'A)_n$ identifiable with exotic spheres, or such that $\partial N$, can be exotic spheres. For such equations local and global existence theorems and stability theorems are obtained.