On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms

Abstract

This paper is concerned with the global solvability of the initial boundary value problem for degenerate quasilinear hyperbolic equations: (1.1) $¥frac{¥partial^{2}u}{¥partial t^{2}}-a(¥int_{¥Omega}|¥nabla u(¥mathrm{x}, t)|^{2}dx)¥Delta u+2¥gamma¥frac{¥partial u}{¥partial t}=0 $ in $¥Omega¥times[0, $ $¥infty) $, (1.2) $u=0 $ on $¥partial¥Omega¥times[0, $ $¥infty) $,