Longtime dynamics of the Kirchhoff equation with strong damping and critical nonlinearity on RN

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Yang, Zhijian¹  Ding, Pengyan¹ 

[1] Zhengzhou Univ, Sch Math & Stat, 100 Sci Rd, Zhengzhou 450001, Peoples R China

关键词: Kirchhoff equation;    Cauchy problem;    Well-posedness;    Global attractor;    Exponential attractor;   

DOI  :  10.1016/j.jmaa.2015.10.013

来源: Elsevier

【 摘 要 】

The paper studies the longtime dynamics of the Kirchhoff equation with strong damping and critical nonlinearity on R-N : u(tt) - Delta u(t) - M(parallel to del u parallel to(2))Delta u-u(t) +g(x, u) f (x). We establish the well-posedness, the existence of the global and exponential attractors in natural energy space H = H-1(R-N) x L-2(R-N) in critical nonlinearity case. These results improve not only the recent ones achieved by Yang (2007) 132], but also ones achieved by Conti, Pata and Squassina (2005) 9] to some extent. (C) 2015 Published by Elsevier Inc.

【 授权许可】

Free