Gradient Decay in the Boltzmann Theory of Non-isothermal Boundary

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-02-06 DOI:10.1007/s00205-024-01956-2

引用次数: 0

Abstract

We consider the Boltzmann equation in a convex domain with a non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belonging 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 quickly as \(t \rightarrow \infty \) .

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非等温边界波尔兹曼理论中的梯度衰减

Abstract 我们考虑了具有漫反射非等温边界的凸域中的玻尔兹曼方程。对于任意 \(p<3\) 的非稳态/稳态问题，我们构建了属于 \(W^{1,p}_x\) 的解。我们证明，在同一 Sobolev 空间中，非稳态解以指数速度收敛于稳态解，当 \(t \rightarrow \infty \) 时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.