Advanced Studies in Mathematical Sciences C

Course title

V0190003

	MATSUZAWA Hiroshi
	TAKEUCHI Shingo

Course description

This course gives an introduction to the maximum principle in the theory of partial differential equations. The maximum principle is a basic and important tool to obtain not only the uniqueness of a solution to the some initial/ boundary value problem of partial differential equations but also the quantitative properties of solutions to some nonlinear partial differential equations.

Purpose of class

The aim of the lecture is to understand the precise statement of the maximum principle for the elliptic and parabolic partial differential equations to get the basic skill to study differential equations.

Goals and objectives

To be able to say the statements of the weak and strong maximum principle of elliptic equations.
To be able to say the statements of the weak and strong maximum principle of parabolic equations.
To be able to explain applications of the maximum principles to the reaction diffusion equations

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Self Check Sheet	Total.
1.	40%	40%
2.	40%	40%
3.	20%	20%
Total.	100%	-

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Introduction : Maximum principle for Harmonic Functions Harmonic functions Mean Value Properties	Review of basic topics related to this class	1330minutes
1.			0minutes
2.	Maximum Principle for harmonic functions.	Not applicable	0minutes
2.	Maximum Principle for harmonic functions.		0minutes
3.	Maximum Principle for Elliptic Equations 1 Linear Elliptic Equations Weak Maximum Principle Hopf Lemma	Not applicable	0minutes
3.			0minutes
4.	Maximum Principle for Elliptic Equations 2 Strong Maximum Principle Phragmen-Lindelof Principle	Not applicable	0minutes
4.			0minutes
5.	Maximum Principle for Parabolic Equations 1 Heat equations Linear Parabolic Equations Weak Maximum Principle	Not applicable	0minutes
5.			0minutes
6.	Maximum Principle for Parabolic Equations 2 Strong Maximum Principle Phragmen-Lindelof Principle	Not applicable	0minutes
6.			0minutes
7.	Application Comparison Principle	Not applicable	0minutes
7.	Application Comparison Principle		0minutes
8.	Not applicable	Not applicable	0minutes
9.	Not applicable	Not applicable	0minutes
10.	Not applicable	Not applicable	0minutes
11.	Not applicable	Not applicable	0minutes
12.	Not applicable	Not applicable	0minutes
13.	Not applicable	Not applicable	0minutes
14.	Not applicable	Not applicable	0minutes
15.	Not applicable	Not applicable	0minutes
Total.	-	-	1330minutes

Evaluation method and criteria

Based on self check sheet(report), if you understand 60% of the content covered in the class, your final score will be 60 points.

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in outside of the class (ScombZ, mail, etc.)

Textbooks and reference materials

Textbook
N/A
The lecture note will be given.

Reference
Evans: Partial Differential Equations(AMS)
Protter and Weinberger: Maximum principles in differential equations(Springer)
Hirokazu Ninomiya: Shinnyu-Denpa and Kakusan Houteishiki(Japanese)(Kyoritu Shuppan)

Prerequisites

Calculus of multivariable functions
Complex Analysis(in particular, Cauchy-Riemann equation)

Office hours and How to contact professors for questions

Before and after lectures I will accept your questions. You can also contact with me via email. My email address will be given in the first lecture.

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge

Active-learning course

N/A

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
N/A	N/A

Education related SDGs:the Sustainable Development Goals

4.QUALITY EDUCATION

Last modified : Wed Mar 19 04:09:26 JST 2025