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.
Students are expected to understand methods for studying reaction-diffusion equations with applications.
Reaction diffusion equation, Traveling wave, Comparison principle
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
Course schedule | Required learning | |
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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. |
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Details will be provided during the lecture.
Students need to submit a report. Details will be announced during the lecture.
Students are required to complete Advanced topics in Analysis A1 (MTH.C405).
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