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

In this paper, we study the following extensible beam equation u(tt) + Delta(2)u - M (parallel to del u parallel to(2)) Delta u + vertical bar u(t)vertical bar(p-1) ut = vertical bar u vertical bar(q-1) u with initial and boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time with positive initial -energy. Keywords: Extensible beam equation, blow up, nonlinear damping term