Yang, Zhijian; Chen, Guowang Blow-up of solutions of a class of generalized Boussinesq equations. (Chinese) Zbl 0960.35090 Acta Math. Sci. (Chin. Ed.) 16, No. 1, 31-39 (1996). Summary: Applying the Fourier transform method, we study the existence of local solutions and the nonexistence of global solutions to initial-boundary value problems for a class of generalized Boussinesq equations: \[ u_{tt}- u_{xx}= bu_{xxxx}+ a(u^p)_{xx}+ cu^q, \] where \(b> 0\), \(a\) and \(c\) are arbitrary real numbers, and \(p\leq 1\), \(q\geq 1\) are integers. We obtain the existence of local solutions to these problems and some sufficient conditions for the blow-up of the solutions within a finite time, and give a few concrete examples. Cited in 1 Document MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35B40 Asymptotic behavior of solutions to PDEs 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) Keywords:existence of local solutions; nonexistence of global solutions; generalized Boussinesq equations PDFBibTeX XMLCite \textit{Z. Yang} and \textit{G. Chen}, Acta Math. Sci. (Chin. Ed.) 16, No. 1, 31--39 (1996; Zbl 0960.35090)