On a final value problem for a biparabolic equation with statistical discrete data

ABSTRACT

This article is devoted to the study of final value problems for biparabolic equation with discrete data in two cases as the linear source and the nonlinear source, respectively. In each of the cases, we show the instability of the solutions and then establish approximate solutions by applying some regularization methods. In addition, the convergence estimates and numerical experiments showing the flexibility of those methods are given.

Keywords:

• Final value problem
• biparabolic equation
• regularized solution
• ill-posed problem

2010 Mathematics Subject Classifications:

• 35K99
• 47J06
• 47H10
• 35K05

Acknowledgments

The authors would like to thank the reviewers and editor for their constructive comments and valuable suggestions that improve the quality of our paper. The author Hoan Luu Cam Vu is supported by Faculty of Basic Science, Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam.

Disclosure statement

No potential conflict of interest was reported by the author(s).