Gradient Decay in the Boltzmann theory of Non-isothermal boundary

2023/04/14 by Hongxu Chen, Chanwoo Kim, Chen, Hongxu +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2304.06933

openalex publication_date 2023/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Boltzmann equation in convex domain with non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belong to W^1,p_x for any p<3. We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially fast as t → ∞.

Cited by

• The Boltzmann equation in an infinite layer: spectrum and asymptotics toward the heat equation
• Optimal C^(1)/(2) regularity of the Boltzmann equation in non-convex domains

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