Reaction-diffusion equations are partial differential equations which mathematically describe the process of time evolution of spatial patterns, and are introduced as mathematical models for various phenomena in Biology, Physics, Chemistry, Population genetics and Neurophysiology. This course is intended to provide a fundamental mathematical theory for the equations. This course will follow "Advanced lectures in Analysis C".
By the end of this course, students will be able to:
1) understand the properties of reaction-diffusion equations,
2) learn the method of analyzing the behavior of solutions.
Reaction-diffusion equation, spatial pattern, stability
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
Course schedule | Required learning | |
---|---|---|
Class 1 | Multi-component reaction-diffusion systems | Details will be provided during each class session. |
Class 2 | Reduction of domains | Details will be provided during each class session. |
Class 3 | Diffusion-induced instability | Details will be provided during each class session. |
Class 4 | Gradient systems | Details will be provided during each class session. |
Class 5 | Lotka-Volterra equations | Details will be provided during each class session. |
Class 6 | FitzHugh-Nagumo equation | Details will be provided during each class session. |
Class 7 | Ginzburg-Landau equation | Details will be provided during each class session. |
Class 8 | Gierer-Meinhardt equation | Details will be provided during each class session. |
None
Eiji Yanagida, Reaction-diffusion equations, University of Tokyo Press
Reports (100%).
Students have passed ZUA.C333 : Advanced courses in Analysis C
yanagida[at]math.titech.ac.jp