Mathematical Analysis for Pattern Formation Problems
We explain our theoretical treatment of various kinds of patterns appearing in nature in this paper. We introduce one of our typical approaches to focus on the pattern boundaries and to derive a curvature flow equation for the motion of these boundaries. This approach is based on the idea that patterns are defined by their boundaries.
KeywordsInterface Curvature flow Reaction-diffusion model
- 1.P. Pelce, Dynamics of Curved Fronts: Perspectives in Physics (Academic Press, New York, 1988)Google Scholar
- 2.B. Lewis, G. von Elbe, Combustion, Flames, and Explosions of Gases. (Academic Press, New York, 1961)Google Scholar
- 3.J.D. Murray, Mathematical Biology, Biomathematics, vol. 19. (Springer, Berlin, 1989)Google Scholar
- 4.A.R. Winfree, When Time Breaks Down. (Princeton University Press, Princeton, 1986)Google Scholar