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Blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term
Author(s) -
Khelghati Ali,
Baghaei Khadijeh
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3623
Subject(s) - mathematics , term (time) , nonlinear system , class (philosophy) , mathematical analysis , order (exchange) , viscous damping , function (biology) , energy method , mathematical physics , calculus (dental) , physics , vibration , finance , quantum mechanics , artificial intelligence , evolutionary biology , computer science , economics , biology , medicine , dentistry
This paper deals with the blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping termu t t − α u x x t + u x x x x = f ( u x ) x , x ∈ Ω , t > 0with Ω = (0,1) and α > 0. Here, f (s) is a given nonlinear smooth function. For 0 < α < p – 1, we prove that the blow‐up occurs in finite time for arbitrary positive initial energy and suitable initial data. This result extends the recent results obtained by Xu et al . (Applicable Analysis)(2013) and Chen and Lu (J. Math. Anal. Appl.)(2009). Copyright © 2015 John Wiley & Sons, Ltd.