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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Sakamoto Shota
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H115)
- Group
- -
- Course number
- MTH.C403
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 3Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
The main subject of this course is a construction of a time-global unique solution to the cutoff Boltzmann equation near an equilibrium.
This course is followed by Advanced topics in Analysis D.
Student learning outcomes
Understanding of the basic theory of the Boltzmann equation, and basic techniques of partial differential equations such as the energy method
Keywords
Boltzmann equation, equations of hydrodynamics, existence and uniqueness of a solution, energy method
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. Occasionally some problems for reports are given.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | The definition of the Boltzmann equation | Details will be provided during each class session. |
| Class 2 | Conservation laws governed by the Boltzmann equation | Details will be provided during each class session. |
| Class 3 | Well-posedness of the cutoff Boltzmann equation near an equilibrium 1: Setting of a problem | Details will be provided during each class session. |
| Class 4 | Well-posedness of the cutoff Boltzmann equation near an equilibrium 2: Properties of linear terms | Details will be provided during each class session. |
| Class 5 | Well-posedness of the cutoff Boltzmann equation near an equilibrium 3: The macro-micro decomposition | Details will be provided during each class session. |
| Class 6 | Well-posedness of the cutoff Boltzmann equation near an equilibrium 4: Bounds of a non-linear term | Details will be provided during each class session. |
| Class 7 | Well-posedness of the cutoff Boltzmann equation near an equilibrium 5: Proof of the main theorem | Details will be provided during each class session. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not required
Reference books, course materials, etc.
Robert T. Glassey, The Cauchy Problem in Kinetic Theory, 1996.
Assessment criteria and methods
Repots (100%)
Related courses
- MTH.C404 ： Advanced topics in Analysis D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Lebesgue integral, basics of functional analysis (not required but helpful)
