Finite Time Blow Up of Solution for 1-D Nonlinear Wave Equation of Sixth Order with Linear Restoring Force at High Energy Level

Abstract

This paper is concerned with the Cauchy problem for some 1-D nonlinear wave equations of sixth order with linear restoring force. By utilizing the concavity method and the technique of anti-dissipativity a finite time blow up result of certain solutions with arbitrarily positive initial energy is presented.