Blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term | Zendy

Khelghati Ali | Zendy; Baghaei Khadijeh | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research