Advanced Partial Differential Equations: Theory and Applications

• Identify functional analytic abstractions in statements of concrete model problems in partial differential equations (PDEs)
• Interpret model problems in functional analytic terms and formally verify prerequisites for such interpretations
• Utilize and apply fundamental functional analytic principles towards analyzing and solving model problems
• Interpret certain computational algorithms in functional analytic terms
• Follow and apply logical strategies of formal mathematical arguments
• Establish the validity mathematical statements about models by constructing and providing formal arguments
• Know and master the relevant mathematical language and be able to communicate abstract and precise mathematical statements and reasoning orally and in writing.
• Know and master advanced topics in functional analysis such as the spectral theorem for compact operators, compact embeddings and the Lax-Milgram Theorem.

The course concerns functional analytic methods for integral and/or partial differential equations. Some specific keywords include: differential operators, Sobolev spaces, elliptic boundary value problems, fixed point theorems, Galerkin method and FEM, and optimization in Hilbert and Banach spaces.

• 6 – 20 (Tues 8-12)

01715/01418, Basic knowledge of partial differential equations and functional analysis

Lectures, theoretical and practical exercises, and oral presentations by students

Minimum: 10.

Please be aware that this course will only be held if the required minimum number of participants is met. You will be informed 8 days before the start of the course, whether the course will be held.