Inverse problems for real principal type operators

IF 1.7 1区 数学 Q1 MATHEMATICS
Lauri Oksanen, Mikko Salo, Plamen Stefanov, Gunther Uhlmann
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引用次数: 0

Abstract

abstract:

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.

实主型算子的逆问题
摘要:我们考虑一般实主型微分算子的逆边界值问题。第一个结果表明,Cauchy 数据集唯一确定了算子的散射关系和低阶系数的双特征射线变换。我们还给出了一般算子的两种不同边界确定方法,并证明了确定非线性实主型方程系数的全局唯一性结果。文章提出了处理输运方程和波方程逆边界问题的统一方法,并强调了奇点传播在解决相关逆问题中的作用。
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
CiteScore
3.20
自引率
0.00%
发文量
35
审稿时长
24 months
期刊介绍: The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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