Article Dans Une Revue Journal of Differential Equations Année : 2023

DIFFUSIVE RELAXATION LIMIT OF THE MULTI-DIMENSIONAL HYPERBOLIC JIN-XIN SYSTEM

Timothée Crin-Barat
Ling-Yun Shou

Résumé

In this paper 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 the 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.

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hal-04862747 , version 1 (03-01-2025)

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Timothée Crin-Barat, Ling-Yun Shou. DIFFUSIVE RELAXATION LIMIT OF THE MULTI-DIMENSIONAL HYPERBOLIC JIN-XIN SYSTEM. Journal of Differential Equations, 2023, 357, pp.302-331. ⟨10.1016/j.jde.2023.02.015⟩. ⟨hal-04862747⟩

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