Direct and inverse problem for the parabolic equation with initial value and time-dependent boundaries. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Li, Heng; Zhou, Jianrong
• Is Part Of: Applicable analysis. Volume 95:Issue 6(2016)
• Page Start: 1307
• Page End: 1326
• Publication Date: 2016-06-02
• Subjects: parabolic equation -- time-dependent boundary -- inverse problem -- numerical approximation -- DCIS; 35K05 -- 35K15 -- 35K20 -- 65M32; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1064111
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we deal with dual problem of a class of non-classical parabolic equations in which the boundaries are time-dependent function instead of fixed values, which arise from Ductal carcinoma in situ (DCIS). In the direct problem part, on using the several transformation and heat potential theory, we established the integral form of solution and proved the existence and uniqueness of solution. Then we consider the inverse problem of finding the control parameter of known moving boundaries, which means determining the potential function of model from incisional biopsy information in the view of DCIS. Algorithm and numerical simulation for both problems are included to demonstrate the validity and applicability of solutions.