MA61051: Modern Theory Of Partial Differential Equation
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| MA61051 | |
|---|---|
| Course name | Modern Theory Of Partial Differential Equation |
| Offered by | Mathematics |
| Credits | 4 |
| L-T-P | 3-1-0 |
| Previous Year Grade Distribution | |
| {{{grades}}} | |
| Semester | Autumn |
Syllabus
Syllabus mentioned in ERP
Prerequisite: PDE, Functional AnalysisTheory of distributions: supports, test functions, regular and singular distributions, generalised derivatives. Sobolev Spaces: definition and basic properties, approximation by smooth functions, dual spaces, trace and imbedding results (without proof).Elliptic Boundary Value Problems: abstract variational problems, Lax-Milgram Lemma, weak solutions and wellposedness with examples, regularity result, maximum principles, eigenvalue problems.Semigroup Theory and Applications: exponential map, C0-semigroups, Hille-Yosida and Lummer-Phillips theorems, applications to heat and wave equations.