Dynamics of Partial Differential Equations

Volume 1 (2004)

Number 1

Global dynamics of nonlinear wave equations with cubic non-monotone damping

Pages: 65 – 86

DOI: https://dx.doi.org/10.4310/DPDE.2004.v1.n1.a3

Author

Yuncheng You (Department of Mathematics, University of South Florida, Tampa, Florida, U.S.A.)

Abstract

For nonlinear wave equations with cubic non-monotone damping, it is proved that the weak solutions exist globally and generate a semiflow. The dissipativity of the semiflow is shown by the asymptotic bootstrap method. Then it is shown that the global weak attractor exists.

Keywords

nonlinear wave equation, non-monotone damping, asymptotic boot-strap method, global weak attractor

2010 Mathematics Subject Classification

Primary 35-xx. Secondary 37-xx.

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Published 1 January 2004