Special lectures on current topics in Mathematics L

Academic unit or major

Graduate major in Mathematics

Instructor(s)

Masaharu Taniguchi / Yoshihiro Tonegawa

Class Format

Lecture

Media-enhanced courses

-

Day of week/Period
(Classrooms)

Class

-

Course Code

MTH.E642

Number of credits

200

Course offered

2026

Offered quarter

4Q

Syllabus updated

Mar 5, 2026

Language

Japanese

Syllabus

Course overview and goals

In this course, the lecturer considers reaction-diffusion equations in the whole Euclidean space, and explains traveling fronts in multi-dimensions. The method is multi-scale methods. For the preparation, the lecturer briefly explains the maximum principles in the whole space, the definitions of supersolutions and subsolutions, and Sattinger's theorem for an application of them. As an application of multi-scale methods, the lecturer explains the V-form traveling fronts in the two-dimensional plane and pyramidal traveling fronts in the general dimensional space. More precisely, he explains the existence and uniqueness of those traveling fronts and the asymptotical stability of them globally in space.

Course description and aims

A student who attends this lecture is expected to learn the following items.
He/she will

learn the definitions of supersolutions and subsolutions;
understand Sattinger's theorem;
learn the multi-scale methods;
study the V-form traveling fronts;
study the pyramidal traveling fronts;
study the properties of these traveling fronts.

Keywords

reaction-diffusion equations, V-form traveling fronts, pyramidal traveling fronts

Competencies

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

Class flow

The lecturer makes explanations on black boards. A student is encouraged to listen the explanations carefully and make questions if necessary.

Course schedule/Objectives

Study advice (preparation and review)

A student is encouraged to ask questions at the lectures. The lecturer will show books or papers for his/her further study if necessary.

Textbook(s)

Students can use the following book. However, one does not have to buy it. The lecturer will give necessary explanations on the black board.

Masaharu Taniguchi
"Traveling Front Solutions in Reaction-Diffusion Equations''
MSJ Memoirs Volume 39, 2021, Mathematical Society of Japan
ISBN: 978-4-86497-097-6

Reference books, course materials, etc.

The lecturer will introduce related papers at his lecture.

Evaluation methods and criteria

Assessment will done by the record of attendance and reports. The subjects will be introduced during the lectures.

Related courses

• MTH.C351 ： Functional Analysis

Prerequisites

None