Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Duruk, N.²  Erbay, H. A.¹  Erkip, A.² 

[1] Isik Univ, Dept Math, TR-34980 Istanbul, Turkey

[2] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey

关键词: Nonlocal Cauchy problem;    Boussinesq equation;    Global existence;    Blow-up;    Nonlocal elasticity;   

DOI  :  10.1016/j.jde.2010.09.002

来源: Elsevier

【 摘 要 】

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite-time blow-up and as well as global existence of solutions of the problem. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free