数学
反向
操作员(生物学)
索波列夫空间
热方程
反问题
类型(生物学)
理论(学习稳定性)
应用数学
数学分析
纯数学
计算机科学
几何学
化学
生态学
生物化学
抑制因子
机器学习
生物
转录因子
基因
作者
Bayan Bekbolat,Daurenbek Serikbaev,Niyaz Tokmagambetov
出处
期刊:Journal of Inverse and Ill-posed Problems
[De Gruyter]
日期:2022-05-31
被引量:1
标识
DOI:10.1515/jiip-2021-0008
摘要
Abstract In this paper, we study non–local in time evolution type equations generated by the Dunkl operator. Direct and inverse problems are investigated with the Caputo time-fractional heat equation with the parameter 0 < γ ≤ 1 {0<\gamma\leq 1} . In particular, well-posedness properties are established for the forward problem. To adopt techniques of the harmonic analysis, we solve the problems in the Sobolev type spaces associated with the Dunkl operator. Our special interest is an inverse source problem for the Caputo–Dunkl heat equation. As additional data, the final time measurement is taken. Since our inverse source problem is ill-posed, we also show the stability result. Moreover, as an advantage of our calculus used here, we derive explicit formulas for the solutions of the direct and inverse problems.
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