scholarly journals Large-time behavior of solutions to a scalar conservation law in several space dimensions

1986 ◽  
Vol 298 (1) ◽  
pp. 401-401 ◽  
Author(s):  
Patricia Bauman ◽  
Daniel Phillips
Keyword(s):  
Conservation Law ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Scalar Conservation Law ◽  
Scalar Conservation

LARGE TIME BEHAVIOR OF NUMERICAL SOLUTIONS OF SCALAR CONSERVATION LAWS

2006 ◽  
Vol 03 (04) ◽  
pp. 631-648
Author(s):  
FRÉDÉRIC LAGOUTIÈRE
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Large Time ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Hyperbolic Conservation ◽  
Periodic Initial Data ◽  
Scalar Conservation

We study the large time behavior of entropic approximate solutions to one-dimensional, hyperbolic conservation laws with periodic initial data. Under mild assumptions on the numerical scheme, we prove the asymptotic convergence of the discrete solutions to a time- and space-periodic solution.

A NONLOCAL CONSERVATION LAW WITH NONLINEAR "RADIATION" INHOMOGENEITY

2008 ◽  
Vol 05 (01) ◽  
pp. 1-23 ◽  
Author(s):  
MARCO DI FRANCESCO ◽  
KLEMENS FELLNER ◽  
HAILIANG LIU
Keyword(s):  
Conservation Law ◽  
Radiation Effects ◽  
Large Time ◽  
Heat Radiation ◽  
Nonlinear Radiation ◽  
Scalar Conservation Law ◽  
Threshold Conditions ◽  
Global Existence And Uniqueness ◽  
Self Similar ◽  
Scalar Conservation

A scalar conservation law with a nonlinear dissipative inhomogeneity, which serves as a simplified model for nonlinear heat radiation effects in high-temperature gases is studied. Global existence and uniqueness of weak entropy solutions along with L1 contraction and monotonicity properties of the solution semigroup is established. Explicit threshold conditions ensuring formation of shocks within finite time is derived. The main result proves — under further assumptions on the nonlinearity and on the initial datum — large time convergence in L1 to the self-similar N-waves of the homogeneous conservation law.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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