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On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms. (English) Zbl 0715.35053

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

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
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