TY - JOUR
T1 - Weak solutions of general systems of hyperbolic conservation laws
AU - Liu, Tai-Ping
AU - Yang, Tong
PY - 2002/10
Y1 - 2002/10
N2 - In this paper, we establish the existence theory for general system of hyperbolic conservation laws and obtain the uniform L1 boundness for the solutions. The existence theory generalizes the classical Glimm theory for systems, for which each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of Lax. We construct the solutions by the Glimm scheme through the wave tracing method. One of the key elements is a new way of measuring the potential interaction of the waves of the same characteristic family involving the angle between waves. A new analysis is introduced to verify the consistency of the wave tracing procedure. The entropy functional is used to study the L1 boundedness.
AB - In this paper, we establish the existence theory for general system of hyperbolic conservation laws and obtain the uniform L1 boundness for the solutions. The existence theory generalizes the classical Glimm theory for systems, for which each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of Lax. We construct the solutions by the Glimm scheme through the wave tracing method. One of the key elements is a new way of measuring the potential interaction of the waves of the same characteristic family involving the angle between waves. A new analysis is introduced to verify the consistency of the wave tracing procedure. The entropy functional is used to study the L1 boundedness.
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U2 - 10.1007/s00220-002-0705-4
DO - 10.1007/s00220-002-0705-4
M3 - 21_Publication in refereed journal
VL - 230
SP - 289
EP - 327
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -