一类带电粒子输运问题解的整体存在性和正则性

IF 0.7 4区工程技术 Q3 MATHEMATICS, APPLIED

Journal of Computational and Theoretical Transport Pub Date : 2021-01-17 DOI:10.1080/23324309.2020.1851722

J. Tervo

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引用次数: 2

摘要

摘要本文考虑了一类模拟带电粒子输运的线性玻尔兹曼输运方程，并以放射治疗剂量计算为例。该方程是精确输运方程的近似，在其碰撞项中包含超奇异积分。本文讨论了空间域G为整个空间的全局情况，利用变分方法给出了该问题解的存在性结果。此外，在相关的各向异性混合范数Sobolev空间尺度上验证了解的一些正则性结果。

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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On Global Existence and Regularity of Solutions for a Transport Problem Related to Charged Particles

Abstract The paper considers a class of linear Boltzmann transport equations which models charged particle transport, for example in dose calculation of radiation therapy. The equation is an approximation of the exact transport equation containing hyper-singular integrals in its collision terms. The paper confines to the global case where the spatial domain G is the whole space Existence results of solutions for the due initial value problem are formulated by applying variational methods. In addition, some regularity results of solutions are verified in scales of relevant anisotropic mixed-norm Sobolev spaces.

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来源期刊

Journal of Computational and Theoretical Transport Mathematics-Mathematical Physics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Emphasizing computational methods and theoretical studies, this unique journal invites articles on neutral-particle transport, kinetic theory, radiative transfer, charged-particle transport, and macroscopic transport phenomena. In addition, the journal encourages articles on uncertainty quantification related to these fields. Offering a range of information and research methodologies unavailable elsewhere, Journal of Computational and Theoretical Transport brings together closely related mathematical concepts and techniques to encourage a productive, interdisciplinary exchange of ideas.