# MATS340 Partial Differential Equations 2 (5 cr)

Study level:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Sobolev spaces and inequalities (review), elliptic partial differential equations in divergence form and their weak solutions, existence of solutions, maximum and comparison principles, uniqueness of solutions, regularity of solutions, parabolic partial differential equations and their weak solutions

## Learning outcomes

After taking the course a student:

• is able to use basic tools of Sobolev spaces in dealing with partial differential equations
• knows the weak definition of a solution to a partial differential equation and can verify in simple cases that a given example is a weak solution
• recognizes elliptic and parabolic partial differential equations and knows applicable existence, uniqueness and regularity results and techiques
• can apply the results for partial differential equations

## Description of prerequisites

MATS230 Partial differential equations, MATS110 Measure and integration theory

## Recommended prerequisites

• Prerequisite group 1

Lecture note

## Literature

• Wu, Yin, Wang: Elliptic and parabolic equations
• Evans: Partial differential equations

## Completion methods

### Method 1

Evaluation criteria:
Grade is based on the points earned from returned exercises.
Select all marked parts

### Method 2

Evaluation criteria:
Points of the final exam.
Select all marked parts
Parts of the completion methods
x

### Participation in teaching (5 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Grade is based on the points earned from homework.
Language:
English, Finnish
Study methods:

Lectures and homework

Study materials:

Lecture note

Literature:
• Evans: Partial differential equations

x

### Exam (5 cr)

Type:
Exam
0-5
Evaluation criteria:
Points of the final exam.
Language:
English, Finnish
Study methods:

Independent study. Final exam.

Study materials:

Lecture notes

No published teaching