Almost global existence for exterior Neumann problems of semilinear wave equations in 2D

TL;DR

This paper proves an almost global existence result for semilinear wave equations with Neumann boundary conditions outside a convex obstacle in 2D, advancing understanding of wave behavior in exterior domains.

Contribution

It establishes an almost global existence theorem for semilinear wave equations with Neumann boundary conditions in exterior 2D domains, a case less studied than Dirichlet conditions.

Findings

Almost global existence for semilinear wave equations in 2D exterior domains

Extension of wave equation theory to Neumann boundary conditions

Insights into wave behavior around convex obstacles

Abstract

The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.