Diffusive relaxation limit of the multi-dimensional Jin-Xin system

Crin-Barat T, Shou LY (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Differential Equations Elsevier

Book Volume: 357

Pages Range: 302-331

DOI: 10.1016/j.jde.2023.02.015

Abstract

We study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a constant state in suitable homogeneous Besov norms, we prove the global well-posedness of strong solutions satisfying uniform estimates with respect to the relaxation parameter. Then, we justify the strong relaxation limit and exhibit an explicit convergence rate of the process. Our proof is based on an adaptation of the techniques developed in [12,13] to be able to deal with additional low-order nonlinear terms.

Authors with CRIS profile

Timothée Crin-Barat Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Nanjing University of Aeronautics and Astronautics (NUAA) / 南京航空航天大学 CN China (CN)

How to cite

APA:

Crin-Barat, T., & Shou, L.Y. (2023). Diffusive relaxation limit of the multi-dimensional Jin-Xin system. Journal of Differential Equations, 357, 302-331. https://doi.org/10.1016/j.jde.2023.02.015

MLA:

Crin-Barat, Timothée, and Ling Yun Shou. "Diffusive relaxation limit of the multi-dimensional Jin-Xin system." Journal of Differential Equations 357 (2023): 302-331.

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