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

2018 ◽  
Vol 121 (2) ◽  
pp. 133-155
Author(s):  
Lianhong Guo ◽  
Yinghui Zhang
Keyword(s):  
Unbounded Domain ◽  
Hyperbolic Equations ◽  
Nonlinear Damping ◽  
Quasilinear Hyperbolic Equations

Boundary effects and large-time behaviour for quasilinear equations with nonlinear damping

2015 ◽  
Vol 145 (5) ◽  
pp. 959-978 ◽  
Author(s):  
Shifeng Geng ◽  
Lina Zhang
Keyword(s):  
Asymptotic Behaviour ◽  
Large Time ◽  
Convergence Rates ◽  
Hyperbolic Equations ◽  
Nonlinear Damping ◽  
Boundary Effects ◽  
Time Behaviour ◽  
Quasilinear Equations ◽  
Quasilinear Hyperbolic Equations ◽  
Quarter Plane

This paper is concerned with the asymptotic behaviour of solutions to quasilinear hyperbolic equations with nonlinear damping on the quarter-plane (x, t) ∈ ℝ+ x ∈ ℝ+. We obtain the Lp (1 ≤ p ≤ +∞) convergence rates of the solution to the quasilinear hyperbolic equations without the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton.

scholarly journals Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Hongjun Qiu ◽  
Yinghui Zhang
Keyword(s):  
Low Temperature ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Initial Perturbation ◽  
Strong Solutions ◽  
Nonlinear Damping ◽  
Decay Rates ◽  
Quasilinear Hyperbolic Equations ◽  
Global Existence And Uniqueness ◽  
Very Low Temperature

We investigate the 3D quasilinear hyperbolic equations with nonlinear damping which describes the propagation of heat wave for rigid solids at very low temperature, below about 20 K. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in the sense of H3-norm. Furthermore, if, additionally, Lp-norm (1≤p<6/5) of the initial perturbation is finite, we also prove the optimal Lp-L2 decay rates for such a solution without the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton.

Sign in / Sign up

Export Citation Format

Share Document