Global existence of solutions for the one-dimensional motions of a compressible viscous gas with radiation: An “infrarelativistic model”

2010 ◽  
Vol 72 (7-8) ◽  
pp. 3258-3274 ◽  
Author(s):  
Bernard Ducomet ◽  
Šárka Nečasová
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Viscous Gas ◽  
One Dimensional ◽  
Global Existence Of Solutions ◽  
Compressible Viscous Gas ◽  
The One

Classical solutions to a dissipative hyperbolic geometry flow in two space variables

2019 ◽  
Vol 16 (02) ◽  
pp. 223-243
Author(s):  
De-Xing Kong ◽  
Qi Liu ◽  
Chang-Ming Song
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Scalar Curvature ◽  
Hyperbolic Geometry ◽  
Existence Of Solutions ◽  
Classical Solutions ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
The One ◽  
Uniformly Bounded

We investigate a dissipative hyperbolic geometry flow in two space variables for which a new nonlinear wave equation is derived. Based on an energy method, the global existence of solutions to the dissipative hyperbolic geometry flow is established. Furthermore, the scalar curvature of the metric remains uniformly bounded. Moreover, under suitable assumptions, we establish the global existence of classical solutions to the Cauchy problem, and we show that the solution and its derivative decay to zero as the time tends to infinity. In addition, the scalar curvature of the solution metric converges to the one of the flat metric at an algebraic rate.

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