# American Institute of Mathematical Sciences

2011, 2011(Special): 1358-1367. doi: 10.3934/proc.2011.2011.1358

## Global existence of solutions for higher order nonlinear damped wave equations

 1 Fukuoka Institute of Technology, Wajiro-higashi, Higashi-ku, Fukuoka, 811-0295, Japan

Received  July 2010 Revised  April 2011 Published  October 2011

We consider a Cauchy problem for a polyharmonic nonlinear damped wave equation. We obtain a critical condition of the nonlinear term to ensure the global existence of solutions for small data. Moreover, we show the op-timal decay property of solutions under the sharp condition on the nonlinear exponents, which is a natural extension of the results for the nonlinear damped wave equations. The proof is based on $L^p-L^q$ type estimates of the fundamental solutions of the linear polyharmonic damped wave equations.
Citation: Hiroshi Takeda. Global existence of solutions for higher order nonlinear damped wave equations. Conference Publications, 2011, 2011 (Special) : 1358-1367. doi: 10.3934/proc.2011.2011.1358
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