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1997 Stiff well-posedness for hyperbolic systems with large relaxation terms (linear constant-coefficient problems)
Jens Lorenz, H. Joachim Schroll
Adv. Differential Equations 2(4): 643-666 (1997).

Abstract

The Cauchy problem for linear constant--coefficient hyperbolic systems $u_t+Au_x=(1/\delta)Bu$ is analyzed. Here $(1/\delta)Bu$ is a large relaxation term, and we are mostly interested in the critical case where $B$ has a nontrivial nullspace. A concept of stiff well--posedness is introduced that ensures solution estimates independent of $0<\delta \leq 1$. Under suitable assumptions, we prove convergence of the $L_2$--solution to a limit as $\delta$ tends to zero. The limit solves a reduced strongly hyperbolic system without zero--order term, the so--called equilibrium system, and we present a method to determine this limit system. For 2$\times$2 systems the requirement of stiff well--posedness is shown to be equivalent to the well--known subcharacteristic condition, but in general the subcharacteristic condition is not sufficient for stiff well--posedness. The theory is illustrated by examples.

Citation

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Jens Lorenz. H. Joachim Schroll. "Stiff well-posedness for hyperbolic systems with large relaxation terms (linear constant-coefficient problems)." Adv. Differential Equations 2 (4) 643 - 666, 1997.

Information

Published: 1997
First available in Project Euclid: 23 April 2013

zbMATH: 1023.35519
MathSciNet: MR1441860

Subjects:
Primary: 35L45
Secondary: 35E20, 47N20, 65M99

Rights: Copyright © 1997 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.2 • No. 4 • 1997
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