2018 Advanced topics in Analysis D

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Graduate major in Mathematics
Instructor(s)
Yanagida Eiji 
Course component(s)
Lecture     
Day/Period(Room No.)
Fri3-4(H137)  
Group
-
Course number
MTH.C404
Credits
1
Academic year
2018
Offered quarter
4Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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 topics in Analysis C".

Student learning outcomes

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.

Keywords

Reaction-diffusion equation, spatial pattern, stability

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Standard lecture course

Course schedule/Required learning

  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.

Textbook(s)

None.

Reference books, course materials, etc.

Eiji Yanagida, Reaction-diffusion equations, University of Tokyo Press

Assessment criteria and methods

Reports (100%).

Related courses

  • MTH.C341 : Differential Equations I
  • MTH.C342 : Differential Equations II
  • MTH.C403 : Advanced topics in Analysis C

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students have passed MTH.C403 : Advanced topics in Analysis C.

Page Top