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

Authors: Lê Xuân Trường, Lê Thị Phương Ngọc, Alain Pham Ngoc Dinh, Nguyễn Thành Long,

https://doi.org/10.1016/j.na.2011.07.015

Publisher, magazine: ,

Publication year: 2011

  Lưu        Trích dẫn         Chia sẻ

Abstract

This paper is devoted to studying a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under the 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.

Tags: Nonlinear wave equation; Local existence; Global existence; Blow up; Exponential decay