# MATS340 Partial Differential Equations 2

### Course info

Due to Covid-19 there are some changes in the spring 2021:

-Recorded lectures that will appear under 'Lectures'

-Exercises are returned and graded through Koppa-system. Remember to allow turnitin so that giving feedback is possible. Thus feedback will be visible through feedback studio. The grade is based on the exercise points (each problem is graded on the scale 0-2):

The course will be graded as follows

50% of exercise points -> grade 1

....

90% of exercise points -> grade 5

Help for the exercises can be obtained through the online 'Teams' Ratkomo, the lecturer follows channel regularly Tue 10-12 and Th 10-12 (former lecture times) but questions can be of course posted any time on the channel. The contact exercise sessions are not held this year. Points are recorded at TIM https://tim.jyu.fi/view/kurssit/matematiikka/mats340-pde2/2021k/pde-2. The course is lectured by

Pablo Blanc, pablo.p.blanc@jyu.fi.

### Course at Sisu

### Course starts

12.01.2021### Course content

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

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

### Prerequisites

Measure and integration 1, Partial differential equations, and also Sobolev spaces is recommended.

### Literature

- Lecture note
- Wu, Yin, Wang: Elliptic and parabolic equations
- Evans: Partial differential equation