Global existence of solutions for higher order nonlinear damped wave equations

Pages: 1358 - 1367, Issue Special, September 2011

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Hiroshi Takeda - Fukuoka Institute of Technology, Wajiro-higashi, Higashi-ku, Fukuoka, 811-0295, Japan (email)

Abstract: 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.

Keywords:  Global solutions, Critical exponents, optimal decay
Mathematics Subject Classification:  Primary: 35A01, 35G25; Secondary: 35B33

Received: July 2010;      Revised: April 2011;      Published: October 2011.