The Calderón Problem for Space-Time Fractional Parabolic Operators with Variable Coefficients

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-03 DOI:10.1137/23m1584137

Agnid Banerjee, Soumen Senapati

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4759-4810, August 2024.
Abstract. We study an inverse problem for variable coefficient fractional parabolic operators of the form [math] for [math] and show the unique recovery of [math] from exterior measured data. Similar to the fractional elliptic case, we use a Runge-type approximation argument, which is obtained via a global weak unique continuation property. The proof of such a unique continuation result involves a new Carleman estimate for the associated variable coefficient extension operator. In the latter part of the work, we prove analogous unique determination results for fractional parabolic operators with drift.

查看原文本刊更多论文

具有可变系数的时空分数抛物线算子的卡尔德龙问题

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4759-4810 页，2024 年 8 月。摘要。我们研究了[math]为[math]形式的可变系数分数抛物线算子的逆问题，并证明了从外部测量数据中恢复[math]的唯一性。与分式椭圆情况类似，我们使用 Runge 型近似论证，通过全局弱唯一延续性质获得。这种唯一延续结果的证明涉及相关变系数扩展算子的新卡勒曼估计。在工作的后半部分，我们证明了具有漂移的分数抛物线算子的类似唯一判定结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.