Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities

Abstract

In this paper, we study the initial boundary value problem for wave equations with combined logarithmic and power-type nonlinearities. For arbitrary initial energy, we prove a necessary and sufficient condition for blow up at infinity of the global weak solutions. In addition, we derive a growth estimate for the blowing up global solutions.

Keywords

• nonlinear wave equation
• combined logarithmic nonlinearities
• blow up at infinity
• necessary and sufficient condition
• growth estimate