Mathematical models for several phenomena in nature are usually nonlinear.
In this lecture, we consider parabolic type PDE, which describes
interface motion. You study some mathematical methods to understand
the properties of the solutions.
In this lecture, we consider parabolic type PDE, which describes
interface motion. You study some mathematical methods to understand
the properties of the solutions.
Understand the properties of solutions to parabolic type PDE and master mathematical methods for them.
- understand mathematical models which describe interface motions
- understand the mathematical methods for analysis to nonlinear parabolic type PDE
- understand the numerical methods for nonlinear PDE
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Introduction: Interface motions | differential equation, dynamical system, numerical analysis | 190minutes |
| 2． | preliminaries for analysis of interface motion | differential equation, dynamical system, numerical analysis and lecture note of previous lecture | 190minutes |
| 3． | Mathematical model of interface motion | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 4． | Curvature flow | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 5． | Properties of solutions to curvature flow | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 6． | Geometric properties of the solutions | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 7． | Numerical method for curvature flow | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 8． | Discussion and presentation 1 | differential equation, dynamical system, numerical analysis and lecture note of previous lectures. prepare the presentation |
190minutes |
| 9． | Blow-up problem | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 10． | Existence of blow-up solution: Fujita-Kaplan's method | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 11． | Existence of blow-up solution: Energy method | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 12． | Numerical method for blow-up problems | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 13． | Summerize mathematical analysis on curvature flow | differential equation, dynamical system, numerical analysis and lecture note of previous lectures | 190minutes |
| 14． | Discussion and presentation on interfrace motion, blow-up problems and several nonlinear problems | differential equation, dynamical system, numerical analysis and lecture note of previous lectures. prepare the presentation |
190minutes |
| Total. | - | - | 2660minutes |
| presentation | report | Total. | |
|---|---|---|---|
| 1. | 15% | 15% | 30% |
| 2. | 15% | 20% | 35% |
| 3. | 15% | 20% | 35% |
| Total. | 45% | 55% | - |
nothing. I introduce corresponding books and papers in the lecture.
differential equations, measure theory, functional analysis, functional equations, numerical analysis, linear algebra, differential
geometry, programing
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicatable |
|---|---|
| N/A | N/A |
Last modified : Thu Mar 21 15:31:47 JST 2019