MATS340 Partial Differential Equations 2 (5–9 cr)
Study level:
Postgraduate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
Content
Sobolev spaces and inequalities, weak derivatives, 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
Completion methods
Returned exercises.
Assessment details
Grade is based on the exercise points as follows:
Grade 1: at least 50 %
Grade 2: at least 60 %
Grade 3: at least 70 %
Grade 4: at least 80 %
Grade 5: at least 90 %
Learning outcomes
After taking the course a student:
-knows different definitions of the Sobolev spaces and recognizes Sobolev functions using them
-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
-can employ regularity techniques for partial differential equations
-knows different definitions of the Sobolev spaces and recognizes Sobolev functions using them
-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
-can employ regularity techniques for partial differential equations
Description of prerequisites
MATS230 Partial differential equations, MATS110 Measure and integration theory
Study materials
Lecture note
Literature
- Wu, Yin, Wang: Elliptic and parabolic equations
- Evans: Partial differential equations
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
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Unpublished assessment item