TY - JOUR
T1 - Convergence of the lax-friedrichs' scheme for equations of isentropic gas dynamics in lagrangian coordinates*'
AU - Lin, Longwei
AU - Yang, Tong
PY - 1991/1/1
Y1 - 1991/1/1
N2 - By compensated compactness theory, Diperna[1,2], Ding, Chen, Luo[3] have solved the equations of elasticity and the equations of isentropic gas dynamics in Euler coordinates with a polytropic equation of state. Their framework essentially depends on the boundedness of the invariant regions of the systems. We now consider the equations of isentropic gas dynamics in Lagrangian coordinates, whose invariant regions are unbounded. Diperna showed that[1]. in order to solve the system, the major step is to find a uniform bound of the difference approximations of the Lax-Friedrichs scheme or a uniform bound of the solutions to the systems with viscous terms. However, it is still an open problem how to find the uniform bounds. © 1991, Taylor & Francis Group. All rights reserved.
AB - By compensated compactness theory, Diperna[1,2], Ding, Chen, Luo[3] have solved the equations of elasticity and the equations of isentropic gas dynamics in Euler coordinates with a polytropic equation of state. Their framework essentially depends on the boundedness of the invariant regions of the systems. We now consider the equations of isentropic gas dynamics in Lagrangian coordinates, whose invariant regions are unbounded. Diperna showed that[1]. in order to solve the system, the major step is to find a uniform bound of the difference approximations of the Lax-Friedrichs scheme or a uniform bound of the solutions to the systems with viscous terms. However, it is still an open problem how to find the uniform bounds. © 1991, Taylor & Francis Group. All rights reserved.
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U2 - 10.1080/03605309108820805
DO - 10.1080/03605309108820805
M3 - RGC 21 - Publication in refereed journal
VL - 16
SP - 1441
EP - 1460
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 8-9
ER -