Learn · NPTEL

Course11110841240 lectures

Advanced Course on Partial Differential Equations - II

Prof. A. K. Nandakumaran Prof. P. S. Datti · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Week 1 Review of Sobolev Spaces

  1. Lec 01 - Introduction and Outline Video
  2. Lec 02 - Review of Sobolev spaces-1 Video
  3. Lec 03 - Review of Sobolev spaces-2 Video
  4. Lec 04 - Review of Sobolev spaces-3 Video
  5. Lec 05 Review of Sobolev spaces-4 Video

Week 2 Elliptic Equations and Weak Formulation

  1. Lec 06 - Review of Sobolev spaces-5 Video
  2. Lec 07 - Elliptic equations and weak formulation Video
  3. Lec 08 - Abstract Formulation Video
  4. Lec 09 Variational Inequality Video
  5. Lec 10 - Babuska-Brezzi Theorem Video

Week 3 Elliptic Equations

  1. Lec 11 Strong vs Weak Form of PDE Video
  2. Lec 12 General Second Order Equations Video
  3. Lec 13 Non-uniqueness of Neumann problem Video
  4. Lec 14 Biharmonic equation, Stokes system Video
  5. Lec 15 Stokes system (continued) Video

Week 4 Elliptic Equations (Continued)

  1. Lec 16 Regularity of Ellptic Equations Video
  2. Lec 17 Regularity Continued Video
  3. Lec 18 Maximum and Minimum Principles for weak formulation Video
  4. Lec 19 Spectrum of the Laplace operator Video
  5. Lec 20 First eigenvalue of the Laplace operator and a brief discussion of a Galerkin method Video

Week 5 Review of unbounded operators

  1. Lec 21 Introduction to semi-groups and unbounded operators Video
  2. Lec 22 Spectrum of an operator Video
  3. Lec 23 Examples of operators and operators in a Hilbert space Video
  4. Lec 24 Perturbation of an operator, Kato theorems. Definition of a semi-group Video
  5. Lec 25 Semi-group and its infinitesimal generator Video

Week 6 Introduction to semi-groups

  1. Lec 26 Examples of semi-groups;spectrum and resolvent of the infinitesimal generator Video
  2. Lec 27 An application. Saturation theorem Video
  3. Lec 28 Hille-Yosida Theorem Video
  4. Lec 29 Lumer-Philips Theorem. Stone's theorem Video
  5. Lec 30 Abstract Cauchy Problem Video

Week 7 Applications to PDE

  1. Lec 31 Semi-group arising from the heat equation Video
  2. Lec 32 Geneartor of the heat semi-group Video
  3. Lec 33 Semi-group arising from the wave equation Video
  4. Lec 34 Semi-group arising from the wave equation in energy space Video
  5. Lec 35 Wave equation in energy space Video

Week 8 Applications to PDE (Continued)

  1. Lec 36 Wave equation in energy space (continued) Video
  2. Lec 37 Semi-group arising from the wave equation in H^1 x L^2 Video
  3. Lec 38 Schroedinger equation in free space Video
  4. Lec 39 Schroedinger equation with a potential. Application of Kato's theorem Video
  5. Lec 40 Equations in a bounded domain. Concluding remarks Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Mathematics
Teacher
Prof. A. K. Nandakumaran Prof. P. S. Datti
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed