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Lax Equivalence for Hyperbolic Relaxation Approximations

Zeyu JinRuo Li
Nov 2023
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摘要原文
This paper investigates the zero relaxation limit for general linear hyperbolic relaxation systems and establishes the asymptotic convergence of slow variables under the unimprovable weakest stability condition, akin to the Lax equivalence theorem for hyperbolic relaxation approximations. Despite potential high oscillations, the convergence of macroscopic variables is established in the strong $L^\infty_t L^2_x$ sense rather than the sense of weak convergence, time averaging, or ensemble averaging.
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