Advanced Course on Partial Differential Equations - II F3KMT4R3NC

URI	`m2://res/F3KMT4R3NC`
Kind	course
Creators	A K Nandakumaran (instructor), P.S. Datti (instructor)
Date	2024-01-17
Scope	in
Ids	course 04dese585:111108412

Expressions

e1: edition

Language	en
Date	2024-01-17

m1: page, IISc Bangalore (record). nptel 111108412
m2: page, 2024-01-17 (record). nptel 111108412

Contents

part 1: Week 1 Review of Sobolev Spaces
session 1: Lec 01 - Introduction and Outline
session 2: Lec 02 - Review of Sobolev spaces-1
session 3: Lec 03 - Review of Sobolev spaces-2
session 4: Lec 04 - Review of Sobolev spaces-3
session 5: Lec 05 Review of Sobolev spaces-4
part 2: Week 2 Elliptic Equations and Weak Formulation
session 6: Lec 06 - Review of Sobolev spaces-5
session 7: Lec 07 - Elliptic equations and weak formulation
session 8: Lec 08 - Abstract Formulation
session 9: Lec 09 Variational Inequality
session 10: Lec 10 - Babuska-Brezzi Theorem
part 3: Week 3 Elliptic Equations
session 11: Lec 11 Strong vs Weak Form of PDE
session 12: Lec 12 General Second Order Equations
session 13: Lec 13 Non-uniqueness of Neumann problem
session 14: Lec 14 Biharmonic equation, Stokes system
session 15: Lec 15 Stokes system (continued)
part 4: Week 4 Elliptic Equations (Continued)
session 16: Lec 16 Regularity of Ellptic Equations
session 17: Lec 17 Regularity Continued
session 18: Lec 18 Maximum and Minimum Principles for weak formulation
session 19: Lec 19 Spectrum of the Laplace operator
session 20: Lec 20 First eigenvalue of the Laplace operator and a brief discussion of a Galerkin method
part 5: Week 5 Review of unbounded operators
session 21: Lec 21 Introduction to semi-groups and unbounded operators
session 22: Lec 22 Spectrum of an operator
session 23: Lec 23 Examples of operators and operators in a Hilbert space
session 24: Lec 24 Perturbation of an operator, Kato theorems. Definition of a semi-group
session 25: Lec 25 Semi-group and its infinitesimal generator
part 6: Week 6 Introduction to semi-groups
session 26: Lec 26 Examples of semi-groups;spectrum and resolvent of the infinitesimal generator
session 27: Lec 27 An application. Saturation theorem
session 28: Lec 28 Hille-Yosida Theorem
session 29: Lec 29 Lumer-Philips Theorem. Stone's theorem
session 30: Lec 30 Abstract Cauchy Problem
part 7: Week 7 Applications to PDE
session 31: Lec 31 Semi-group arising from the heat equation
session 32: Lec 32 Geneartor of the heat semi-group
session 33: Lec 33 Semi-group arising from the wave equation
session 34: Lec 34 Semi-group arising from the wave equation in energy space
session 35: Lec 35 Wave equation in energy space
part 8: Week 8 Applications to PDE (Continued)
session 36: Lec 36 Wave equation in energy space (continued)
session 37: Lec 37 Semi-group arising from the wave equation in H^1 x L^2
session 38: Lec 38 Schroedinger equation in free space
session 39: Lec 39 Schroedinger equation with a potential. Application of Kato's theorem
session 40: Lec 40 Equations in a bounded domain. Concluding remarks

Catalogue records

nptel: 111108412 (manifestation)
nptel_video: 111108412 (manifestation)