IST - Partial Differential Equations (2022)
Speakers and Syllabus
| Speakers | |
| Prof. G.D. Veerappa Gowda, Raja Ramanna Fellow TIFR Centre for applicable Mathematics, Sharada Nagar, Chikkabommasandra, Bengaluru, 560065 |
Prof. P. S. Datti, |
| Prof. A Adimurthi, TIFR Centre for Applicable Mathematics, Sharada Nagar, Chikkabommasandra, Bengaluru, 560065 |
Prof. A. K. Nandakumaran, Indian Institute of Science Bangaluru |
| Course associates/ Tutors | |
| Prof. Rajib Haloi Department of Applied Sciences, Tezpur University, Napaam, Assam 784028 |
Dr. Jayanta Borah Department of Mathematical Sciences, Tezpur University, Napaam, Assam 784028 |
Detailed syllabus and the topics to be covered by each speaker
| SlNo | Name of thespeaker | Topic of lectures | Number of lectures with tutorials |
| 1. | Prof. G.D. Veerappa Gowda | First order linear and non-linear PDE:Method of characteristics. Hamilton Jacobi equations: Legendre transform and Hopf-Lax formula. Conservation laws:weak solutions, shocks and entropy conditions, Riemann problems and Lax-Oleinik formula. | 6(L) 6(T) |
| 2. | Prof. P. S. Datti | Laplace equation: Fundamental solution, mean value formulas,Green’s functions. Heat equation: Fundamental solution, initial value problems and properties of solutions. Wave equation: D ’Alembert’s formula, Solution by spherical means in higher dimensions. Non-homogeneous problem. | 6(L) 6(T) |
| 3. | Prof. A.K. Nandakumaran | Sobolev spaces: Definition and basic properties of weak derivatives. Test functions and distributions, Sobolev spaces, Approximation by smooth functions, Imbedding theorems, Compactness theorems, Trace theorems and Sobolev inequalities. | 6(L) 6(T) |
| 4. | Prof. A Adimurthi | Elliptic equations: Variational Problems, Lax-Milgram theorem, Regularity theorem, Maximum principles, Eigenvalue problems. | 6(L) 6(T) |
| 5. | Dr. Jayanta Borah | Course/Tutorial associates. | 24(T) |
| 6. | Prof. Rajib Haloi | Course/Tutorial associates. | 24(T) |
Time Table
Tentative time-table:
| Schedule for the first week | |||||||
| Date/Day | 9:30 to 11:00 | Tea Break | 11:30 to 1: 00 | Lunch Break | 3:00 to 4:00 | Tea Break | 4:30 to 5:30 |
| 21.11.2022 | AKN | PSD | T1 AKN, JB,RH |
T2 PSD, RH,JB |
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| 22.11.2022 | PSD | AKN | T3 PSD, RH,JB |
T4 AKN, JB,RH |
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| 23.11.2022 | AKN | PSD | T5 AKN, JB,RH |
T6 PSD, RH,JB |
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| 24.11.2022 | PSD | AKN | T7 PSD, RH,JB |
T8 AKN, JB,RH |
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| 25.11.2022 | AKN | PSD | T9 AKN, JB,RH |
T 10 PSD, RH,JB |
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| 26.11.2022 | PSD | AKN | T11 PSD, RH,JB |
T12 AKN, JB,RH |
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| Schedule for the second week | |||||||
| 28.11.2022 | AM | Tea Break | GDV | Lunch Break | T1 AM, RH,JB |
Tea Break | T2 GDV, JB,RH |
| 29.11.2022 | GDV | AM | T3 GDV, JB,RH |
T4 AM, RH,JB |
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| 30.11.2022 | AM | GDV | T5 AM, RH,JB |
T6 GDV, JB,RH |
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| 01.12.2022 | GDV | AM | T7 GDV, JB,RH |
T8 AM, RH,JB |
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| 02.12.2022 | AM | GDV | T9 AM, RH,JB |
T10 GDV, JB, RH |
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| 03.12.2022 | GDV | AM | T11 GDV, JB, RH |
T12 AM,RH, JB |
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Legends:
- AM: Prof. A Adimurthi
- GDV: Prof. G. D. Veerppa Gowda
- RH: Prof. Rajib Haloi
- AKN: Prof. A. K. Nandakumaran
- PSD: Prof. P. S. Datti
- JB: Jayanta Borah