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- Academic unit or major
- Mathematics
- Instructor(s)
- Tonegawa Yoshihiro Kan Toru
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H201)
- Group
- -
- Course number
- ZUA.C332
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 2Q
- Syllabus updated
- 2017/4/12
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
The aim is to learn methods for studying nonlinear partial differential equations through the analysis of travelling waves of bistable reaction-diffusion equations. First, in one-dimensional space, the construction of a travelling wave by a phase plane analysis and the stability analysis by a comparison principle are performed. Then, as a non-planar travelling wave, a V-shaped traveling wave in two-dimensional space is discussed.
This course follows Advanced courses in Analysis A.
Student learning outcomes
Students are expected to understand methods for studying reaction-diffusion equations with applications.
Keywords
Reaction diffusion equation, Traveling wave, Comparison principle
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 | Bistable reaction-diffusion equations | Details will be provided during each class session. |
| Class 2 | A comparison principle and the monotone iterative method | Details will be provided during each class session. |
| Class 3 | One-dimensional travelling waves 1 | Details will be provided during each class session. |
| Class 4 | One-dimensional travelling waves 2 | Details will be provided during each class session. |
| Class 5 | One-dimensional travelling waves 3 | Details will be provided during each class session. |
| Class 6 | V-shaped traveling waves 1 | Details will be provided during each class session. |
| Class 7 | V-shaped traveling waves 2 | Details will be provided during each class session. |
| Class 8 | V-shaped traveling waves 3 | Details will be provided during each class session. |
Textbook(s)
None in particular
Reference books, course materials, etc.
Details will be provided during the lecture.
Assessment criteria and methods
Students need to submit a report. Details will be announced during the lecture.
Related courses
- ZUA.C331 ： Advanced courses in Analysis A
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to complete Advanced courses in Analysis A (ZUA.C331).
Other
None in particular
