Sharp critical thresholds in a hyperbolic system with relaxation

Manas Bhatnagar; Hailiang Liu

doi:10.3934/dcds.2021098

Article Contents

2021, Volume 41, Issue 12: 5851-5869. Doi: 10.3934/dcds.2021098 open access

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Sharp critical thresholds in a hyperbolic system with relaxation

Manas Bhatnagar and
Hailiang Liu^,

Department of Mathematics, Iowa State University, Ames, IA 50011, USA

Received: November 30, 2020

Revised: April 30, 2021

Early access: July 2021

Published: December 2021

This research was supported by the National Science Foundation under Grant DMS1812666

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Abstract

We propose and study a one-dimensional $ 2\times 2 $ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different classes of relaxation we identify intrinsic critical thresholds for initial data that distinguish global regularity and finite time blowup. For relaxation independent of density, we estimate bounds on density in terms of velocity where the system is strictly hyperbolic.

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Mathematics Subject Classification: Primary: 35L65;Secondary: 35B30.

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Figure 1. Terminal roots of $ f(u)-u = 0 $

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Figure 2. Asymptotic invariant region

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