تقرير
Strong relaxation limit and uniform time asymptotics of the Jin-Xin model in the $L^{p}$ framework
| العنوان: | Strong relaxation limit and uniform time asymptotics of the Jin-Xin model in the $L^{p}$ framework |
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| المؤلفون: | Crin-Barat, Timothée, Shou, Ling-Yun, Zhang, Jianzhong |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35L40, 35L45, 35K55 |
| الوصف: | We investigate the diffusive relaxation limit and the time-asymptotic stability of the Jin-Xin model toward viscous conservation laws in $\mathbb{R}^d$ with $d\geq1$. First, we establish uniform regularity estimates with respect to both the time and the relaxation parameter $\varepsilon>0$, for initial data in hybrid Besov spaces based on general $L^{p}$-norms. This uniformity enables us to derive $\mathcal{O}(\varepsilon)$ bounds on the difference between solutions of the viscous conservation law and its associated Jin-Xin approximation, thus justifying the strong convergence of the Jin-Xin hyperbolic relaxation. Furthermore, under an additional condition on the initial data, for instance, that the low frequencies belong to $L^{p/2}(\mathbb{R}^{d})$, we show that the $L^{p}(\mathbb{R}^d)$-norm of the solution to the Jin-Xin model decays at the optimal rate $(1+t)^{-d/{2p}}$ while the $L^{p}(\mathbb{R}^d)$-norm of its difference with the solution of the associated viscous conservation law decays at the enhanced rate $\varepsilon(1+t)^{-d/{2p}-1/2}$. Comment: 39 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.04105 |
| رقم الأكسشن: | edsarx.2311.04105 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |