The 3D quasilinear hyperbolic equations with nonlinear damping in a general unbounded domain

We consider 3D quasilinear hyperbolic equations with nonlinear damping on a general unbounded domain with a slip boundary condition, which describes the propagation of a heat wave for rigid solids at very low temperature, below about 20K. The global existence and uniqueness of classical solutions is obtained when the initial data is near the equilibrium. We also investigate convergence rates of the system in the half-space. We prove that the classical solution converges to a constant steady state at the L-2-rate (1 + t)(-3/4).