Approximation of an Inverse Initial Problem for a Biparabolic Equation

In this paper, we consider the problem of finding the initial distribution for the linear inhomogeneous and nonlinear biparabolic equation. The problem is severely ill-posed in the sense of Hadamard. First, we apply a general filter method to regularize the linear nonhomogeneous problem. Then, we also give a regularized solution and consider the convergence between the regularized solution and the sought solution. Under the a priori assumption on the exact solution belonging to a Gevrey space, we consider a generalized nonlinear problem by using the Fourier truncation method to obtain rigorous convergence estimates in the norms on Hilbert space and Hilbert scale space. © 2018, Springer International Publishing AG, part of Springer Nature.

Authors
Nguyen H.T.1 , Kirane M. 2, 3, 4 , Quoc N.D.H.6 , Vo V.A.5
Publisher
Birkhauser Verlag AG
Number of issue
1
Language
English
Status
Published
Number
18
Volume
15
Year
2018
Organizations
  • 1 Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh, Viet Nam
  • 2 LaSIE, Facult des Sciences et Technologies, Universi de La Rochelle, Avenue M. Crpeau, La Rochelle Cedex, 17042, France
  • 3 NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
  • 4 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
  • 5 Faculty of General Sciences, Can Tho University of Technology, Can Tho, Viet Nam
  • 6 Department of Science Management, Thu Dau Mot University, Thu Dau Mot, Binh Duong, Viet Nam
Keywords
Backward problem; Biparabolic equation; Error estimate; Regularization method
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6885/