Another way of solving a free boundary problem related to DCIS model. Issue 15 (18th November 2021)

• Record Type: Journal Article
• Authors: Zhou, Jianrong; Xu, Yongzhi; Li, Heng
• Is Part Of: Applicable analysis. Volume 100:Issue 15(2021)
• Page Start: 3244
• Page End: 3258
• Publication Date: 2021-11-18
• Subjects: Free boundary problem -- Adomian decomposition method (ADM) -- parabolic equation -- ductal carcinoma in situ (DCIS) model -- approximation solution; 35K05 -- 35K20 -- 35Q68 -- 35R30 -- 35R35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1715369
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider a free boundary problem related to ductal carcinoma in situ (DCIS) model. Existence and uniqueness theorem is proved by using Banach fixed point theorem. For computation part, the decomposition method of Adomian is first implemented to get an approximate solution of intermediate function v ( x, t ), which satisfies a nonlinear equation with initial boundary value conditions, and then based on relationships between v ( x, t ) and s ( t ), numerical solutions s ~ ( t ) of free boundary s ( t ) are obtained. The approximate solution u ~ ( x, t ) can be straightly derived by applying Adomian decomposition method to the linear equation involving u ( x, t ) . Finally, a numerical example is presented to show the validity and applicability of our method.