BLOW UP OF POSITIVE INITIAL-ENERGY SOLUTIONS FOR THE EXTENSIBLE BEAM EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

Abstract

In this work, we study the following extensible beam equation

u_{tt}+△²u-M(‖∇u‖²)△u+|u_{t}|^{p-1}u_{t}=|u|^{q-1}u

with initial and boundary condition. Under suitable conditions on the initial datum, we prove that the solution blow up in finite time with positive initial-energy.