2022 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis C
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shota Sakamoto
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Fri (H115)
- Class
- -
- Course Code
- MTH.C403
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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. |
Study advice (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.
Evaluation methods and criteria
Repots (100%)
Related courses
- MTH.C404 ： Advanced topics in Analysis D
Prerequisites
Lebesgue integral, basics of functional analysis (not required but helpful)