AIS - Hyperbolic Conservation Laws (2024)
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
T. Raja Shekhar IIT Kharagpur |
10 |
Method of characteristics applied to first-order linear, semilinear, and quasilinear equations, A brief introduction to the theory of distributions, Sobolev spaces, and functions of bounded variations |
|
Ujjwal Koley TIFR CAM, Bangalore |
10 |
The notion of hyperbolicity and examples, Nonlinear first order PDE. Hamilton-Jacobi equations and conservation laws: Notion of weak solutions, Lax-Oleinik formula, uniqueness, and entropy conditions |
|
Rajib Dutta IISER Kolkata |
10 |
Vanishing viscosity method, notion of Kruzhkov entropy solutions, travelling waves for scalar conservation laws. |
|
Manas Ranjan Sahoo NISER Bhubaneswar |
10 |
Wave front tracking method for scalar conservation laws and hyperbolic systems(with an emphasis on 2\times 2 system) |
|
Anupam Pal Choudhury NISER Bhubaneswar |
10 |
Diperna’s measure valued solutions. Initial-boundary value problems for scalar conservation laws and first order hyperbolic systems. |
|
Tanmay Sarkar IIT Jammu |
10 |
Numerical methods for hyperbolic conservation laws, Conservative methods, Lax-Wendroff theorem, Godunov’s method, Riemann’s solver and TVD methods. |
References:
-
Shock Waves and Reaction-Diffusion Equations: Joel Smoller
-
Hyperbolic Conservation laws in Continum Physics: Constantine M. Dafermos
-
Hyperbolic Systems of Conservation laws: Philippe G. LeFloch
-
Front Tracking for Hyperbolic Conservation Laws: Helge Holden and Nils Henrik Risebro
-
Partial Differential Equation: Lawrence C. Evans
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Abhishek Das |
NISER, Bhubaneswar |
|
2 |
Abhrojyoti Sen |
IISER Pune |
|
3 |
Balakrishna Chhatria |
IIT Kharagpur |
|
4. |
Mukul Dwivedi |
IIT Jammu |
|
5. |
Anirban Das |
TIFR CAM |
|
6. |
Kanchan Dwivedi |
NIT Warangal |
Time Table
Time-Table (with names of speakers and course associates/tutors):
| Day | Date | Lecture 1&2 (9.30–11.00) |
Tea (11.00 – 11.25) |
Tutorial (11.30–12.30) |
Lunch (12.30– 2.25) |
Lecture 3&4 (2.30– 4.00) |
Tea and Snacks (4.00 - 4.25) |
Tutorial (4.30-5.30) |
| (name of the speaker) | (name of the speaker + tutors) | (name of the speaker) | (name of the speaker + tutors) | |||||
| Mon | Week1 | TRS | TRS & BC | UK | UK & AD2 | |||
| Tues | TRS | TRS & BC | UK | UK & AD2 | ||||
| Wed | TRS | TRS & BC | UK | UK &AD 2 | ||||
| Thu | TRS | TRS & BC | UK | UK & AD2 | ||||
| Fri | TRS | TRS & BC | UK | UK&AD2 | ||||
| Sat | TRS | TRS & BC | UK | UK&AD2 | ||||
| Mon | Week2 | RD | RD & KD | MRS | MRS& AS | |||
| Tues | RD | RD & KD | MRS | MRS & AS | ||||
| Wed | RD | RD& KD | MRS | MRS & AS | ||||
| Thu | RD | RD & KD | MRS | MRS & AS | ||||
| Fri | RD | RD& KD | MRS | MRS & AS | ||||
| Sat | RD | RD& KD | MRS | MRS&AS | ||||
| Mon | Week3 | TS | TS& MD | APC | APC& AD1 | |||
| Tues | TS | TS& MD | APC | APC& AD1 | ||||
| Wed | TS | TS& MD | APC | APC& AD1 | ||||
| Thu | TS | TS& MD | APC | APC& AD1 | ||||
| Fri | TS | TS& MD | APC | APC& AD1 | ||||
| Sat | TS | TS& MD | APC | APC &AD1 |
TRS: T. Raja Shekhar BC: Balakrishna Chhatria
UK: Ujjwal Koley MD: Mukul Dwivedi
RD: Rajib Dutta AD2: Anirban Das
MRS: Manas Ranjan Sahoo KD: Kanchan Dwivedi
APC: Anupam Pal Choudhury
TS: Tanmay Sarkar
AD1: Abhishek Das
AS: Abhrojyoti Sen