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.
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页码：1937 / 1956
页数：20
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