Source identification problems for abstract semilinear nonlocal differential equations

Nguyen Thi Van Anh; Bui Thi Hai Yen

doi:10.3934/ipi.2022030

Article Contents

2022, Volume 16, Issue 5: 1389-1428. Doi: 10.3934/ipi.2022030

This issue Previous Article On multiple scattering in Compton scattering tomography and its impact on fan-beam CT Next Article

Source identification problems for abstract semilinear nonlocal differential equations

Nguyen Thi Van Anh^1,2, , and
Bui Thi Hai Yen^3,

1.
Department of Mathematics, Hanoi National University of Education, No. 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
2.
Institute of Mathematics, Vietnam Academy of Science and Technology, No. 18 Hoang Quoc Viet, Hanoi, Vietnam
3.
Department of Mathematics, Hoa Lu University, Ninh Nhat, Ninh Binh, Vietnam

^*Corresponding author: Nguyen Thi Van Anh
^*Corresponding author: Nguyen Thi Van Anh

Received: September 2021

Revised: May 2022

Early access: June 2022

Published: October 2022

This research is funded by the Simons Foundation Grant Targeted for Institute of Mathematics, Vietnam Academy of Science and Technology

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Abstract

In this paper, we investigate a source identification problem for a class of abstract nonlocal differential equations in separable Hilbert spaces. The existence of mild solutions and strong solutions for the problem of identifying parameter are obtained. Furthermore, we study the continuous dependence on the data and the regularity of the mild solutions and strong solutions of nonlocal differential equations. Examples given in anomalous diffusion equations illustrate the existence and regularity results.

Keywords:

Mathematics Subject Classification: Primary: 34G20, 34K29, 35R11, 47N20; Secondary: 93B30.

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