Hyperbolic conservation laws with stiff relaxation terms and entropy

Communications on Pure and Applied Mathematics - Tập 47 Số 6 - Trang 787-830 - 1994
Gui‐Qiang Chen1, C. David Levermore2, Tai‐Ping Liu3
1University-of Chicago
2University of Arizona
3Stanford University

Tóm tắt

Abstract

We study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N × N systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown to be interlaced with those of the original system. Moreover, the first correction to the reduced system is shown to be dissipative. A partial converse is proved for 2 × 2 systems. This structure is then applied to study the convergence to the reduced dynamics for the 2 × 2 case. © 1994 John Wiley & Sons, Inc.

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Thông tin xuất bản

Communications on Pure and Applied Mathematics

Tập 47 Số 6

787-830

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