An attractor for the singularly perturbed Kirchhoff equation with supercritical nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Li, Ke¹  Wei, Hongjun¹ 

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

关键词: Kirchhoff equation;    Global attractor;   

DOI  :  10.1016/j.jmaa.2013.09.013

来源: Elsevier

【 摘 要 】

We consider a quasilinear wave equation of Kirchhoff type epsilon u(tt) - (1 + parallel to del u parallel to(2))Delta u + u(t) + f(u) = g(x), where epsilon > 0 is a small parameter. Without any growth restrictions on the nonlinearity f (u), we prove the existence of a finite-dimensional global attractor on an appropriate (bounded) phase space. The key step is the estimate of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. (C) 2013 Elsevier Inc. All rights reserved.

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