Nishihara, Kenji; Yamada, Yoshio On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms. (English) Zbl 0715.35053 Funkc. Ekvacioj, Ser. Int. 33, No. 1, 151-159 (1990). The authors consider the evolution equation \[ u''(t)-\| A^{1/2}u(t)\|^{2\alpha}Au(t)+2\gamma u'(t)=0 \] for symmetric positive definite operators A with discrete spectrum and compact inverse. Using the approximation method of Galerkin along with some uniform a priori bounds, they establish the existence of weak solutions for a corresponding initial-value problem. Some asymptotic decay estimates are also included. Reviewer: M.Tarabek Cited in 1 ReviewCited in 50 Documents MSC: 35L80 Degenerate hyperbolic equations 35L70 Second-order nonlinear hyperbolic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs Keywords:global solutions; Galerkin method; existence; decay estimates PDFBibTeX XMLCite \textit{K. Nishihara} and \textit{Y. Yamada}, Funkc. Ekvacioj, Ser. Int. 33, No. 1, 151--159 (1990; Zbl 0715.35053)