On the construction of analytic solutions for a diffusion-reaction equation with a discontinuous switch mechanism

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:231

Article

Vermolen, F. J.¹  Javierre, E.² 

[1] Delft Univ Technol, Delft Inst Appl Math, NL-2628 CD Delft, Netherlands

[2] Univ Zaragoza, CIBER BBN, Grp Struct Mech & Mat Modelling, Zaragoza 50018, Spain

关键词: Wound healing;    Discontinuous switch mechanism;    Analytic solutions;    Moving boundary;    Existence and uniqueness;   

DOI  :  10.1016/j.cam.2009.05.022

来源: Elsevier

【 摘 要 】

The existence of waiting times, before boundary motion sets in, for a diffusion-diffusion reaction equation with a discontinuous switch mechanism. is demonstrated. Limit cases of the waiting times are discussed in mathematical rigor. Further, analytic Solutions for planar and circular wounds are derived. The waiting times, as predicted using these analytic solutions, are perfectly between the derived bounds. Furthermore, it is demonstrated by both physical reasoning and mathematical rigor that the movement of the boundary can be delayed once it starts moving. The proof of this assertion resides oil Continuity and monotonicity arguments. The theory sustains the construction of analytic Solutions. The model is applied to simulation of biological processes with a threshold behavior, such as wound healing or tumor growth. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free