On the initial-boundary problem for fourth order wave equations with damping, strain and source terms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Wang, Yanjin²  Wang, Yufeng¹ 

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China

关键词: Fourth order wave equation;    Blow-up;    Global existence;    Arbitrary initial energy;    Energy decay;   

DOI  :  10.1016/j.jmaa.2013.03.060

来源: Elsevier

【 摘 要 】

In this paper we study the global existence and blow-up of solutions to the fourth order equations u(tt) + u(t) + Delta(2)u - alpha Delta u - Sigma(n)(i=1) partial derivative/partial derivative x(i)(theta(i)(u(xi))) = f(u), x is an element of Omega, t > 0, where alpha <= 0. Under appropriate assumptions on the initial data and parameters in the above equation we establish two results on blow-up of solutions with arbitrary initial energy, -infinity < E(0) < +infinity. Also, by using a potential well we show the global existence of solutions for the fourth order wave equation with some theta(i)(s) and f (s). Especially, it is proved that the energy decays exponentially as t -> infinity. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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