Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

TL;DR

This paper investigates a nonlinear wave equation with two-point boundary conditions, establishing conditions for finite-time blow-up and exponential decay of solutions, supported by numerical results.

Contribution

It provides new theoretical results on existence, blow-up, and decay for a nonlinear wave equation with two-point boundary conditions, including numerical validation.

Findings

Weak solutions with negative initial energy blow up in finite time

Conditions for global existence and exponential decay are established

Numerical results support theoretical findings

Abstract

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results