scholarly journals An extension of Bakhvalov’s theorem for systems of conservation laws with damping

2017 ◽  
Vol 14 (04) ◽  
pp. 703-719
Author(s):  
Hermano Frid
Keyword(s):  
Periodic Solution ◽  
Initial Data ◽  
Conservation Laws ◽  
Gas Dynamics ◽  
Global Solutions ◽  
Eulerian Formulation ◽  
Systems Of Conservation Laws ◽  
Periodic Initial Data ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

For [Formula: see text] systems of conservation laws satisfying Bakhvalov conditions, we present a class of damping terms that still yield the existence of global solutions with periodic initial data of possibly large bounded total variation per period. We also address the question of the decay of the periodic solution. As applications, we consider the systems of isentropic gas dynamics, with pressure obeying a [Formula: see text]-law, for the physical range [Formula: see text], and also for the “non-physical” range [Formula: see text], both in the classical Lagrangian and Eulerian formulation, and in the relativistic setting. We give complete details for the case [Formula: see text], and also analyze the general case when [Formula: see text] is small. Further, our main result also establishes the decay of the periodic solution.

scholarly journals Soluciones globales para sistema isotérmico con fuente

2021 ◽  
Vol 39 (1) ◽  
Author(s):  
Xian Ting Wang
Keyword(s):  
Global Existence ◽  
Gas Dynamics ◽  
Short Note ◽  
Global Solutions ◽  
Momentum Equation ◽  
Global Existence Of Solutions ◽  
Existence And Stability ◽  
Isothermal System ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x,t,ρ,u)=b(x,t)ρ+(a′(x)/a(x))*ρu^2+α(x,t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.

Nonlinear Stability Of The Difference Schemes For Equations Of Isentropic Gas Dynamics

2008 ◽  
Vol 8 (2) ◽  
pp. 155-170 ◽  
Author(s):  
P. MATUS ◽  
A. KOLODYNSKA
Keyword(s):  
Initial Data ◽  
Numerical Experiment ◽  
Difference Scheme ◽  
Nonlinear Stability ◽  
Gas Dynamics ◽  
Differential Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas ◽  
The Difference ◽  
Theoretical Results

AbstractFor the difference scheme approximating the gas dynamics problem in Riemann invariants a priory estimates with respect to the initial data have been obtained. These estimates are proved without any assumptions about the solution of the differential problem using only limitations for the initial and boundary conditions. Estimates of stability in the general case have been obtained only for the finite instant of time. The uniqueness and convergence of the difference solution are also considered. The results of the numerical experiment confirming theoretical results are given.

LARGE TIME DECAY OF SOLUTIONS TO ISENTROPIC GAS DYNAMICS WITH SPHERICAL SYMMETRY

2009 ◽  
Vol 06 (02) ◽  
pp. 371-387
Author(s):  
NAOKI TSUGE
Keyword(s):  
Spherical Symmetry ◽  
Gas Dynamics ◽  
Large Time ◽  
Approximate Solutions ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Time Decay ◽  
Decay Of Solutions ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

We consider the large time behavior of solutions to isentropic gas dynamics with spherical symmetry. In the present paper, we show the decay of the pressure in particular. To do this, we investigate approximate solutions constructed by a difference scheme.

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