TY - JOUR
T1 - Identifying an unknown source term in a time-space fractional parabolic equation
AU - Van Thang, Nguyen
AU - Van Duc, Nguyen
AU - Minh, Luong Duy Nhat
AU - Thành, Nguyen Trung
N1 - Publisher Copyright:
© 2021 IMACS
PY - 2021/8
Y1 - 2021/8
N2 - An inverse problem of identifying an unknown space-dependent source term in a time-space fractional parabolic equation is considered in this paper. Under reasonable boundedness assumptions about the source function, a Hölder-type stability estimate of optimal order is proved. To regularize the inverse source problem, a mollification regularization method is applied. Error estimates of the regularized solution are proved for both a priori and a posteriori rules for choosing the mollification parameter. A direct numerical method for solving the regularized problem is proposed and numerical examples are presented to illustrate its effectiveness.
AB - An inverse problem of identifying an unknown space-dependent source term in a time-space fractional parabolic equation is considered in this paper. Under reasonable boundedness assumptions about the source function, a Hölder-type stability estimate of optimal order is proved. To regularize the inverse source problem, a mollification regularization method is applied. Error estimates of the regularized solution are proved for both a priori and a posteriori rules for choosing the mollification parameter. A direct numerical method for solving the regularized problem is proposed and numerical examples are presented to illustrate its effectiveness.
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U2 - 10.1016/j.apnum.2021.04.016
DO - 10.1016/j.apnum.2021.04.016
M3 - Article
AN - SCOPUS:85105696406
SN - 0168-9274
VL - 166
SP - 313
EP - 332
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -