AIS Differential Equations (2018)

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Venue: School of Mathematics and Statistics,  Hyderabad, Telangana
Date:  4th, Jun 2018 to 23rd, Jun 2018

 

School Convener(s)

Name T Suman Kumar R Radha
Mailing Address Assistant Professor
School of Mathematics and Statistics
University of Hyderabad
Professor
School of Mathematics and Statistics
University of Hyderabad

 


 Speakers with their affiliations:

Sr. Speaker Affiliation
1 V. D. Sharma IIT Bombay
2 R Radha University of Hyderabad
3 G.D. Veerappa Gowda TIFR-CAM
4 A. Adimurthi TIFR-CAM
5 S. Baskar IIT Bombay
6 Shyam Ghoshal TIFR-CAM

 


 Syllabus:

Sr. Speaker Topics covered
1 V. D. Sharma
  • Scalar conservation laws, hyperbolic equations, weak solutions, Method of characteristics, R-H condition, non-uniqueness of weak solution, entropy conditions, irreversibility
2

R Radha

  • Explained existence and uniqueness of solution to differential equations, the Stability theory for ordinary differential equations, Lyapunov energy functional, one dimensional bifurcation theory, along with types of bifurcations.
3 A.Adimuthi
  • Topics on Hamilton-Jacobi equations, Lagendre transformation, Hopf-Lax formula, Lax-Oleinik formula, Structure theorem for bounded entropy solutions, conservation laws with discontinuous flux, interface entropy condition, uniqueness of (A,B)-entropy solution, L 1 stability
4 G Veerappa Gowda
  • Lectures on Finite difference equations, consistency, stability of numerical schemes, convergence of numerical solutions, conservative schemes, Lax-Wendroff’s theorem, Lax-Friedrichs scheme, Godunov scheme, Engquist-Osher scheme, monotone schemes, Godunov’s theorem, TVD schemes, l 1contraction schemes, numerical entropy inequality
5 S. Baskar
  • Derivation derivation of Euler system for gas dynamics and also given the shallow water wave system.After introducing the method of characteristics, the compatibility condition is derived. Using this,it is shown that the classical solution may not remain constant along the characteristics especially in the case of quasi-linear systems. Taking this as a motivation, Riemann invariants are derived for isentropic flow and shallow water waves. In the case of 2x2 system the invertibility of the map is shown between the solution and the Riemann invariant. Using Riemann invariants, full details of the breakdown of a classical solution in a 2x2 system is discussed and derived sufficient conditions for gradient catastrophe. As an outcome of this derivation, the genuinely nonlinear and linearly degenerate characteristic fields are defined. The theory of simple waves for general systems are discussed where we have characterized the simple waves in terms of the Riemann invariants. Construction of a solution of the Riemann problem for a general system in 1D is explained along with the local existence and uniqueness theorem for a weak solution of the Riemann problem for a general system in one dimensional. Finally, the idea of Glimm approach of constructing approximation solutions to a general initial value problem by using Riemann problem solutions as building blocks is briefly explained.
6 Shyam Ghoshal
  • lectures on System of conservation laws, R-H condition, Lax-entropy condition, shock and rarefaction waves, entropy solutions of the Cauchy problem, continuous dependence of solutions, uniqueness of entropy solutions for systems and Vanishing viscosity approximation of conservation laws, uniform BV estimates, l ∞ estimates for the solution, uniqueness of an entropy solution respectively.

 

 


 Time Table

  Date 09:30
to
11:00
11:00
to
11:30
11:30
to
13:00
13:00
to
14:00
14:00
to
15:00
15:00
to
15:30
15:30
to
16:30
First
Week
4.6.2018 VDS T
E
A
 
 
B
R
E
A
K
VDS L
U
N
C
H

B
R
E
A
K

Tutorial T
E
A
 
 
B
R
E
A
K
Tutorial
5.6.2018 VDS VDS Tutorial Tutorial
6.6.2018 VDS VDS Tutorial Tutorial
7.6.2018 RR RR Tutorial Tutorial
8.6.2018 RR RR Tutorial Tutorial
9.6.2018 RR RR Tutorial Tutorial
Second
Week
11.6.2018 GDV AA Tutorial Tutorial
12.6.2018 GDV AA Tutorial Tutorial
13.6.2018 GDV AA Tutorial Tutorial
14.6.2018 GDV AA Tutorial Tutorial
15.6.2018 GDV AA Tutorial Tutorial
16.6.2018 GDV AA Tutorial Tutorial
Third
Week
18.6.2018 SB SG Tutorial Tutorial
19.6.2018 SB SG Tutorial Tutorial
20.6.2018 SB SG Tutorial Tutorial
21.6.2018 SB SG Tutorial Tutorial
22.6.2018 SB SG Tutorial Tutorial
23.6.2018 SB SG Tutorial Tutorial
VDS Prof V D Sharma,IIT Bombay
RR Prof R radha, University of Hyderabad
GDV Prof G D Veerappa Gowda, TIFR-CAM, Bangalore
AA Prof A Adimurthi, TIFR-CAM, Bangalore
SB Dr S Baskar, IIT Bombay
SH Dr Shyam Ghosal, TIFR-CAM

 


List of Participants

Sr. Name of the Participan Affiliation
1 Ms. Saraswati Shah Delhi University, Delhi
2 Ms. Deepti Kaur University of Delhi, Delhi
3 Ms. Mythili Narayanaswamy TIFR CAM, Bangalore
4 Mrs. Anshu Yadav IIT, Delhi
5 Ms. Ruchika Lochab Delhi Technological University, Delhi
6 Arijit Hazra TIFR-CAM Bangalore
7 Mr. Deepak Bhoriya IIT, Delhi
8 Mr. Naresh Kumar IIT, Guwahati
9 Dr. Avijit Sarkar University of Kalyani, West Bengal
10 Mr. Anupam Sen IIT-Kharagpur, West Bengal
11 Mr. Chhatra Pal ARSD College, University of Delhi, Delhi
12 Mr. Hirak Doshi Sri Sathya Sai Institute of Higher Learning, Puttaparti
13 Mr. Govind Mahato, IIT-ISM Dhanbad
14 Mr. Joydev Halder University of Hyderabad
15 Dr. Bhargav Kumar TIFR-CAM, Banglore
16 Dr. Ganesh TIFR-CAM, Banglore
17 Dr Animesh TIFR-CAM, Banglore
18 Dr T Shukla IIT Kanpur

 

 


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