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Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System

Crin-Barat T., L. Shou. Diffusive Relaxation Limit of the Multi-Dimensional Hyperbolic Jin-Xin System (2022)

Abstract. 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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Last updated on September 29, 2022

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Last Publications

Control of neural transport for normalizing flows

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

Gaussian Beam ansatz for finite difference wave equations

Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave

Optimal design of sensors via geometric criteria

  • Control of neural transport for normalizing flows
  • A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
  • Gaussian Beam ansatz for finite difference wave equations
  • Optimal design of sensors via geometric criteria
  • Eigenvalue bounds for the Gramian operator of the heat equation
  • Control of neural transport for normalizing flows
  • A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
  • Gaussian Beam ansatz for finite difference wave equations
  • Optimal design of sensors via geometric criteria
  • Eigenvalue bounds for the Gramian operator of the heat equation
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