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 ${\mathbb{R}}^3.$ 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.

中文翻译：

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关于带电粒子输运问题解的全局存在性和规律性

摘要

该论文考虑了一类线性玻尔兹曼传输方程，它模拟带电粒子传输，例如在放射治疗的剂量计算中。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。该论文仅限于空间域G是整个空间的全局情况${\mathbb{电阻}}^3.$应用变分方法制定了到期初值问题解的存在性结果。此外，在相关各向异性混合范数 Sobolev 空间的尺度上验证了解的一些规律性结果。