Blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term

This paper deals with the blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term urn:x-wiley:mma:media:mma3623:mma3623-math-0046 with Ω = (0,1) and α > 0. Here, f(s) is a given nonlinear smooth function. For 0 < α < p – 1, we prove that the blow‐up occurs in finite time for arbitrary positive initial energy and suitable initial data. This result extends the recent results obtained by Xu et al. (Applicable Analysis)(2013) and Chen and Lu (J. Math. Anal. Appl.)(2009). Copyright © 2015 John Wiley & Sons, Ltd.