Premium
Regularization of a backward problem for the inhomogeneous time‐fractional wave equation
Author(s) -
Huy Tuan Nguyen,
Au Vo,
Nhat Huynh Le,
Zhou Yong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6285
Subject(s) - mathematics , regularization (linguistics) , bounded function , a priori and a posteriori , wave equation , backus–gilbert method , well posed problem , rate of convergence , mathematical analysis , inverse problem , regularization perspectives on support vector machines , tikhonov regularization , philosophy , channel (broadcasting) , epistemology , artificial intelligence , computer science , electrical engineering , engineering
In this paper, we consider a backward problem for an inhomogeneous time‐fractional wave equation in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the initial density of substance, but we can observe the density at a positive moment. The existence and regularity for the backward problem are investigated. The backward problem is ill‐posed, and we propose a regularizing scheme by using a modified regularization method. We also prove the convergence rate for the regularized solution by using some a priori regularization parameter choice rule.