# AIS Linear Partial Differential Equations (2017)- Speakers and Syllabus

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 KTIFR CAM Bangalore 5 x 1.5 = 7.5 hrs First order PDE: Solutions by characteristics, Classification of 2nd order PDEs. Distribution theory, Sobolev spaces. Dr. Ujjwal KoleyTIFR CAM Bangalore 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 GhoshalTIFR CAM Bangalore 5 x 1.5 = 7.5 hrs Heat equation: Fundamental Solution, Mean value formula, Properties of solutions, Energy methods. Prof. G. D. Veerappa GowdaTIFR CAM Bangalore 4 x 1.5 + 2 x 1.0 = 8.0 hrs Wave equation: Solution by spherical means, Non-homogeneous problem, Energy methods. Prof. AdimurthiTIFR CAM Bangalore 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 BanerjeeTIFR CAM Bangalore 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 BiswasTIFR CAM Bangalore 5 x 1.5 = 7.5 hrs Second order parabolic equations: Existence of weak solutions, Regularity, Maximum principles. Prof. K. T. JosephTIFR CAM Bangalore 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

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
1. Arka Mallick (AM)
2. Manmohan Vashisth (MV)
3. Arnab Roy (AR)