Global existence and asymptotic behaviour of solutions for a class of fourth order strongly damped nonlinear wave equations

Runzhang, Xu; Yanbing, Yang

doi:10.1090/S0033-569X-2012-01295-6

Authors: Xu Runzhang and Yang Yanbing
Journal: Quart. Appl. Math. 71 (2013), 401-415
MSC (2010): Primary 35L25, 35A01, 35L30
DOI: https://doi.org/10.1090/S0033-569X-2012-01295-6
Published electronically: October 23, 2012
MathSciNet review: 3112820
Full-text PDF Free Access

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Abstract: In this paper we study the initial boundary value problem for a class of fourth order strongly damped nonlinear wave equations $u_{tt}-\Delta u+ \Delta ^2 u-\alpha \Delta u_t=f(u)$ . By introducing a family of potential wells we prove the existence of global weak solutions and global strong solutions under some weak growth conditions on . Furthermore we give the asymptotic behaviour of solutions.

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