کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4641229 1341299 2009 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the construction of analytic solutions for a diffusion–reaction equation with a discontinuous switch mechanism
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On the construction of analytic solutions for a diffusion–reaction equation with a discontinuous switch mechanism
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 231, Issue 2, 15 September 2009, Pages 983–1003
نویسندگان
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