A blow-up result for a higher-order nonlinear Kirchhoff-type hyperbolic equation

Abstract

In this work we consider a multi-dimensional higher-order Kirchhoff-type wave equation, with Dirichlet boundary conditions. We establish a blow-up result for certain solutions with positive initial energy.

A blow-up result for Kirchhoff-type equations with high energy

“…On the other hand, Galaktionov and Pohozaev [12] studied the Cauchy problem for the higher order Kirchhoff-type equations, and obtained some nonexistence results of the solutions. In [13] Messaoudi and Said-Houari considered also a multidimensional higher-order Kirchhoff-type equations with Dirichlet boundary conditions, and by using the potential well method they established a blow-up result for certain solutions with positive initial energy. There are also more results to other Kirchhoff-type equations (see [14--17] and the references therein).…”

Existence, Decay, and Blow-Up of Solutions for a Higher-Order Kirchhoff-Type Equation with Delay Term

“…He also established the blow-up result for E ð0Þ < 0. Later, in 2007, Messaoudi and Houari [18] obtained the blow-up of solutions with E ð 0Þ > 0 of the equation (6). Then, Piskin and Polat [19] considered global existence and decay estimates utilizing Nakao's inequality of the equation (6).…”

Global existence and blowup of solutions for a class of nonlinear higher-order wave equations

“…A problem similar to (1.1) have also been discussed by Li [20], where global existence and blow-up results were established. The blow-up result of Li [20] was later improved by Messaoudi and Said-Houari [21], where a blow-up result was established for certain solutions with positive initial energy. For the general case, Ye [1] investigated problem (1.1) and showed the solution exists global if the initial energy is sufficiently small.…”