Arbitrary initial energy blow up for fourth-order viscous damped wave equation with exponential-type growth nonlinearity

Abstract This letter is concerned with the following damped nonlinear wave equation with exponential nonlinearity u t t + Δ 2 u + u + Δ 2 u t + u t = f ( u ) in Ω × ( 0 , ∞ ) where the nonlinearity f is a regular function satisfying f ( 0 ) = 0 with an exponential growth to fix later. The above wave problem describes a class of essential nonlinear evolution equations appearing in the elastic–plastic-microstructure models. In this letter blow up result is established for arbitrary initial energy with the viscous damping terms.