Syllabus

MA61051
Course name	Modern Theory Of Partial Differential Equation
Offered by	Mathematics
Credits	4
L-T-P	3-1-0
Previous Year Grade Distribution
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Semester	Autumn

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.

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