Postgraduate Course: MIGS: Elliptic and Parabolic PDEs (MATH11210)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||This course covers parabolic and elliptic equations. Useful methods to study solutions such as travelling wave and similarity solutions are developed and nonexistence and multiplicity results for solutions of nonlinear elliptic problems are studied by a variety of methods. Different concepts and tools are developed such as maximum principles, blow up and comparison theorems. One striking result that will be proved is that positive solutions of autonomous semilinear elliptic problems on a ball must be radially symmetric.
The remaining lectures are on variational formulation of elliptic PDEs. The material includes an introduction to the Sobolev function spaces, Sobolev embedding and trace theorems.
- Analysis of parabolic and elliptic PDEs (including existence, uniqueness, maximum principles, energy estimates, monotone iteration, regularity, eigenfunctions)
- Variational theory of PDEs
- Sobolev embeddings and trace theorems
The aim is to learn new things to get a broad education in the area as a basis for a wide range of PhD projects and for post-PhD employment. Unless otherwise noted, the details of the content of these courses can be found on the Scottish Mathematical Sciences Training Centre web site www.smstc.ac.uk
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Course Delivery Information
|Academic year 2021/22, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Programme Level Learning and Teaching Hours 3,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
|No Exam Information
On completion of this course, the student will be able to:
- Thoroughly understand the analytical concepts and methods developed in the uniqueness and existence theorems for solutions of PDEs.
- Apply finite element approximations to solve PDEs.
|Graduate Attributes and Skills
|Course organiser||Prof Benedict Leimkuhler
|Course secretary||Mrs Katy Cameron
Tel: (0131 6)50 5085