Identification of the initial condition in backward problem with nonlinear diffusion and reaction

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Vo Van Au^1,2  Nguyen Huy Than³ 

[1] Vietnam Natl Univ, Univ Nat Sci, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

[2] Can Tho Univ Technol, Fac Gen Sci, Can Tho City, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

关键词: Quasi-reversibility method;    Backward problem;    Parabolic equation;    Regularization;   

DOI  :  10.1016/j.jmaa.2017.02.055

来源: Elsevier

【 摘 要 】

In this paper, we study the backward in time problem for nonlinear parabolic equations associated with nonlinear diffusion coefficient. The problem is ill-posed in the sense of Hadamard. Under an a priori assumption on the exact solution in Gevrey space, we propose a new regularization method for stabilising the ill-posed problem. Our results extend some earlier works on backward problems for nonlinear parabolic equations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free