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BV‐estimates of Lax–Friedrichs' scheme for hyperbolic conservation laws with relaxation
Author(s) -
Zhang Jing,
Zhu Changjiang
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.954
Subject(s) - conservation law , mathematics , uniqueness , relaxation (psychology) , scheme (mathematics) , hyperbolic partial differential equation , simple (philosophy) , zero (linguistics) , mathematical analysis , partial differential equation , psychology , social psychology , philosophy , linguistics , epistemology
In this paper, we will give BV‐estimates of Lax–Friedrichs' scheme for a simple hyperbolic system of conservation laws with relaxation and get the global existence and uniqueness of BV‐solution by the BV‐estimates above. Furthermore, our results show that the solution converge towards the solution of an equilibrium model as the relaxation time ε>0 tends to zero provided sub‐characteristic condition holds. Copyright © 2007 John Wiley & Sons, Ltd.