# Coursebooks

## Parabolic and hyperbolic PDE's

English

#### Remarque

pas donné en 2019/20

#### Summary

1. PARABOLIC EQUATIONS: Existence and uniqueness of weak-solutions, Maximum principle. Fundamental solutions. Infinite speed of propagation. 2. HYPERBOLIC EQUATIONS: Existence and uniqueness of weak solutions. Fundamental solutions. Finite speed of propagation.

#### Content

I. PARABOLIC EQUATIONS

1. Existence and uniqueness of weak-solutions.

2. Maximum principle.

3. Fundamental solutions. Infinite speed of propagation.

4. Separation of variables for a rectangle domains. The asymptotic behaviour of solutions as time goes to infinity.

II. HYPERBOLIC EQUATIONS

1. One dimensional investigation.

2. Existence and uniqueness of weak solutions.

3. Fundamental solutions.

4. Finite speed of propagation.

5. Separation of variables for a rectangle domains. The asymptotic behaviour of solutions as time goes to infinity.

#### Learning Prerequisites

##### Required courses

MATH-407: Elliptic PDE's.

#### Teaching methods

To balance the theoretical part, sometimes one hour of exercices is replaced of one hour of class.

#### Assessment methods

Exam written

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

### In the programs

• Mathematics - master program, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Parabolic and hyperbolic PDE's
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Parabolic and hyperbolic PDE's
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Parabolic and hyperbolic PDE's
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

### legend

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• Lecture in French
• Lecture in English
• Lecture in German