On the Existence of Global Solutions for a Nonlinear Klein-Gordon Equation

Polat N., Taskesen H.

FILOMAT, vol.28, no.5, pp.1073-1079, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.2298/fil1405073p
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1073-1079
  • Keywords: Klein-Gordon equation, Potential well, Global existence, High energy initial data, TIME BLOW-UP, CAUCHY-PROBLEM, INSTABILITY
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The aim of this work is to study the global existence of solutions for the Cauchy problem of a Klein-Gordon equation with high energy initial data. The proof relies on constructing a new functional, which includes both the initial displacement and the initial velocity: with sign preserving property of the new functional we show the existence of global weak solutions.