The school aims to give a thorough introduction to linear partial differential equations including various techniques to solve them. The school is basically addressed to the research students in Indian institutes and universities with interest in pursuing research in partial differential equations and related topics.
Syllabus:
| Name of the Speakers with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Prof. Sandeep K |
5 x 1.5 = 7.5 hrs |
First order PDE: Solutions by characteristics, Classification of 2nd order PDEs. Distribution theory, Sobolev spaces. |
|
Dr. Ujjwal Koley |
5 x 1.5 = 7.5 hrs |
Laplace’s equation: Fundamental solution, Mean value formulas, Properties of harmonic functions, Green’s function, Energy methods. |
|
Dr. Shyam Sundar Ghoshal |
5 x 1.5 = 7.5 hrs |
Heat equation: Fundamental Solution, Mean value formula, Properties of solutions, Energy methods. |
|
Prof. G. D. Veerappa Gowda |
4 x 1.5 + 2 x 1.0 = 8.0 hrs |
Wave equation: Solution by spherical means, Non-homogeneous problem, Energy methods. |
|
Prof. Adimurthi |
4 x 1.5 + 2 x 1.0 = 8.0 hrs
|
Second order elliptic equations: Existence of weak solutions, Lax-Milgram theorem, Energy estimates, Fredholm alternative, Interior (boundary) regularity. |
|
Dr. Agnid Banerjee |
4 x 1.5 + 2 x 1.0 = 8.0 hrs |
Second order elliptic equations: Maximum principles, Weak and strong maximum principles, Harnack’s inequality, Eigenvalues of symmetric (non-symmetric) elliptic operators. |
|
Dr. Imran Biswas |
5 x 1.5 = 7.5 hrs
|
Second order parabolic equations: Existence of weak solutions, Regularity, Maximum principles. |
|
Prof. K. T. Joseph |
4 x 1.5 + 2 x 1.0 = 8.0 hrs |
Second order hyperbolic equations: Existence of weak solutions, Regularity, Propagation of disturbances, Equations in two variables. |
References:
1. Partial differential equations — L. C. Evans
2. The analysis of linear partial differential operators — L. Hörmander
3. Lectures on linear partial differential equations — L. Nirenberg
Time-Table (with names of the speakers and tutors ):
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05–11.25) |
Lecturer 2 (11.30–1.00) |
Lunch (1.05–2.25) |
Tutorial (2.30–3.30) |
Tea (3.35-3.55) |
Tutorial (4.00-5.00) |
Snacks 5.30 |
|
|
|
(name of the speaker) |
|
(name of the speaker) |
|
(name of the speaker & tutor) |
|
(name of the speaker & Tutor) |
|
|
Mon |
June 19 |
SK |
|
UK |
|
SK |
|
AR |
|
|
Tues |
June 20 |
SK |
|
UK |
|
SK |
|
AR |
|
|
Wed |
June 21 |
SK |
|
UK |
|
AM |
|
AR |
|
|
Thu |
June 22 |
SK |
|
UK |
|
AM |
|
AR |
|
|
Fri |
June 23 |
GDV |
|
UK |
|
AM |
|
AR |
|
|
Sat |
June 24 |
GDV |
|
SG |
|
AM |
|
AR |
|
|
Sunday : Off |
|||||||||
|
Mon |
June 26 |
GDV |
|
SG |
|
GDV |
|
AR |
|
|
Tues |
June 27 |
GDV |
|
SG |
|
GDV |
|
AR |
|
|
Wed |
June 28 |
AA |
|
SG |
|
AA |
|
AR |
|
|
Thu |
June 29 |
AA |
|
SG |
|
AA |
|
AR |
|
|
Fri |
June 30 |
AA |
|
AB |
|
AM |
|
MV |
|
|
Sat |
July 01 |
AA |
|
AB |
|
AM |
|
MV |
|
|
Sunday : Off |
|||||||||
|
Mon |
July 03 |
KTJ |
|
AB |
|
AM |
|
MV |
|
|
Tues |
July 04 |
KTJ |
|
AB |
|
AM |
|
MV |
|
|
Wed |
July 05 |
IB |
|
AB |
|
KTJ |
|
MV |
|
|
Thu |
July 06 |
IB |
|
KTJ |
|
KTJ |
|
MV |
|
|
Fri |
July 07 |
IB |
|
KTJ |
|
AM |
|
MV |
|
|
Sat |
July 08 |
IB |
|
IB |
|
AM |
|
MV |
|
1. Prof. Adi Adimurhti (AA)
2. Dr. Agnid Banerjee (AB)
3. Dr. Imran Biswas (IB)
4. Dr. Shyam Ghoshal (SG)
5. Prof. G. D. Veerappa Gowda (GDV)
6. Prof. Sandeep K (SK)
7. Prof. K. T. Joseph (KTJ)
8. Dr. Ujjwal Koley (UK)
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Arka Mallick |
PhD Student at TIFR CAM |
|
2 |
Manmohan Vashisth |
PhD Student at TIFR CAM |
|
3 |
Arnab Roy |
PhD Student at TIFR CAM |
- Arka Mallick (AM)
- Manmohan Vashisth (MV)
- Arnab Roy (AR)