Stable Determination of Time-Dependent Collision Kernel in the Nonlinear Boltzmann Equation

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-09-17 DOI:10.1137/23m1604060

Ru-Yu Lai, Lili Yan

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1937-1956, October 2024.
Abstract. We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions [math]. 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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稳定确定非线性玻尔兹曼方程中与时间有关的碰撞核

SIAM 应用数学杂志》，第 84 卷第 5 期，第 1937-1956 页，2024 年 10 月。摘要。我们考虑了非线性玻尔兹曼方程在维数 [math] 中的逆问题，该问题具有随时间变化的核。在某些附加条件下，我们通过测量建立了碰撞核的对数型稳定性结果。作为稳定性结果的直接结果，我们还推导出了唯一性结果。我们的方法依赖于二阶线性化和多元有限差分，以及光射线变换的稳定性。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.