Learn · Advanced Course on Partial Differential Equations - II
Lecture 3 of 40Week 1 Review of Sobolev Spaces
Lec 03 - Review of Sobolev spaces-2
Prof. A. K. Nandakumaran Prof. P. S. Datti · IISc Bangalore
Credits and licence
- From
- Advanced Course on Partial Differential Equations - II, IISc Bangalore (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Lec 01 - Introduction and Outline
- Lec 02 - Review of Sobolev spaces-1
- Lec 03 - Review of Sobolev spaces-2
- Lec 04 - Review of Sobolev spaces-3
- Lec 05 Review of Sobolev spaces-4
- Lec 06 - Review of Sobolev spaces-5
- Lec 07 - Elliptic equations and weak formulation
- Lec 08 - Abstract Formulation
- Lec 09 Variational Inequality
- Lec 10 - Babuska-Brezzi Theorem
- Lec 11 Strong vs Weak Form of PDE
- Lec 12 General Second Order Equations
- Lec 13 Non-uniqueness of Neumann problem
- Lec 14 Biharmonic equation, Stokes system
- Lec 15 Stokes system (continued)
- Lec 16 Regularity of Ellptic Equations
- Lec 17 Regularity Continued
- Lec 18 Maximum and Minimum Principles for weak formulation
- Lec 19 Spectrum of the Laplace operator
- Lec 20 First eigenvalue of the Laplace operator and a brief discussion of a Galerkin method
- Lec 21 Introduction to semi-groups and unbounded operators
- Lec 22 Spectrum of an operator
- Lec 23 Examples of operators and operators in a Hilbert space
- Lec 24 Perturbation of an operator, Kato theorems. Definition of a semi-group
- Lec 25 Semi-group and its infinitesimal generator
- Lec 26 Examples of semi-groups;spectrum and resolvent of the infinitesimal generator
- Lec 27 An application. Saturation theorem
- Lec 28 Hille-Yosida Theorem
- Lec 29 Lumer-Philips Theorem. Stone's theorem
- Lec 30 Abstract Cauchy Problem
- Lec 31 Semi-group arising from the heat equation
- Lec 32 Geneartor of the heat semi-group
- Lec 33 Semi-group arising from the wave equation
- Lec 34 Semi-group arising from the wave equation in energy space
- Lec 35 Wave equation in energy space
- Lec 36 Wave equation in energy space (continued)
- Lec 37 Semi-group arising from the wave equation in H^1 x L^2
- Lec 38 Schroedinger equation in free space
- Lec 39 Schroedinger equation with a potential. Application of Kato's theorem
- Lec 40 Equations in a bounded domain. Concluding remarks