Research ArticleNo Access

Existence of optimal solution to the problem of finding an initial condition for nonlinear diffusion from integral observations

Nguyen Thi Ngoc Oanh

Thai Nguyen University of Sciences, Tan Thinh, Thai Nguyen, Vietnam

E-mail Address: oanhntn.tn@gmail.com

Corresponding author.

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and

Le Thi Thu Giang

Thuongmai University, 79 Ho Tung Mau, Cau Giay, Hanoi, Vietnam

E-mail Address: lethugiang@tmu.edu.vn

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https://doi.org/10.1142/S1793557121501424Cited by:2 (Source: Crossref)

Abstract

In this paper, we study the problem of reconstructing an unknown initial condition for nonlinear diffusion from integral observations which have many practical meanings. We reformulate this problem as a variational one to minimizing objective functional. We prove the existence of this minimized problem in our main result.

Communicated by B. K. Dass

Keywords:

AMSC: 35K05, 35K58, 49J20

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