Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 190, Issue 1, Pages 131-149Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/S0022-0396(03)00014-7
Keywords
hyperbolic PDE; nonconcave flux; relaxation; equilibrium; extended entropy; monotone scheme
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We establish global solutions of nonconcave hyperbolic equations with relaxation arising from traffic flow. One of the characteristic fields of the system is neither linearly degenerate nor genuinely nonlinear. Furthermore, there is no dissipative mechanism in the relaxation system. Characteristics travel no faster than traffic. The global existence and uniqueness of the solution to the Cauchy problem are established by means of a finite difference approximation. To deal with the nonconcavity, we use a modified argument of Oleinik (Amer. Math. Soc. Translations 26 (1963) 95). It is also shown that the zero relaxation limit of the solutions exists and is the unique entropy solution of the equilibrium equation. (C) 2003 Elsevier Science (USA). All rights reserved.
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