کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641229 | 1341299 | 2009 | 21 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On the construction of analytic solutions for a diffusion–reaction equation with a discontinuous switch mechanism On the construction of analytic solutions for a diffusion–reaction equation with a discontinuous switch mechanism](/preview/png/4641229.png)
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 on 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.
Journal: Journal of Computational and Applied Mathematics - Volume 231, Issue 2, 15 September 2009, Pages 983–1003