# American Institute of Mathematical Sciences

## A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term

 Università di Cagliari, Dipartimento di Matematica e Informatica, Viale Merello 92, 09123 Cagliari, Italy

* Corresponding author: Monica Marras

To our friend Patrizia on the occasion of her sixty-fifth birthday.

Received  September 2018 Revised  September 2018 Published  November 2019

In this paper we study a initial-boundary value problem for 4th order hyperbolic equations with weak and strong damping terms and superlinear source term. For blow-up solutions a lower bound of the blow-up time is derived. Then we extend the results to a class of equations where a positive power of gradient term is introduced.

Citation: Monica Marras, Stella Vernier-Piro. A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020157
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