Large time behavior of global solutions of the semilinear clamped beam equation with slowly decaying data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:423

Article

Takeda, Hiroshi

关键词: Damped beam equation;    Cauchy problem;    Slowly decaying data;    Fourth order wave equation with damping;    Asymptotic profile;    Perturbation;   

DOI  :  10.1016/j.jmaa.2014.10.032

来源: Elsevier

【 摘 要 】

We discuss the existence of the global solution and its asymptotic profile for the Cauchy problem for the nonlinear damped beam equation. We show that the equation admits a unique global solution with small slowly decaying data e.g. (1 + x(2))(-k/2), 0 < k <= 1. Moreover we show that the solution can be approximated by the solution of the linear heat equation with suitable data. The proof is based upon the estimate for the evolution operator of the linearized equation in the homogeneous Sobolev space. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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