STABLE DETERMINATION OF TIME-DEPENDENT COLLISION KERNEL IN THE NONLINEAR BOLTZMANN EQUATION

被引：0

作者：

Lai, Ru-yu ^{[1
]}

Yan, Lili ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2024年 / 84卷 / 05期

基金：

美国国家科学基金会;

关键词：

inverse problems; nonlinear Boltzmann equation; logarithmic stability; time-dependent collision kernel; NONSTATIONARY TRANSPORT-EQUATION; INVERSE PROBLEM; ELLIPTIC-EQUATIONS; STABILITY; COEFFICIENTS; SCATTERING; RECONSTRUCTION; UNIQUENESS;

D O I：

10.1137/23M1604060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an inverse problem for the nonlinear Boltzmann equation with a time- dependent kernel in dimensions n \geq 2. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization and multivariate finite differences, as well as the stability of the light-ray transform.

引用

页码：1937 / 1956

页数：20

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