Non linear hyperbolic conservation laws play a central role in science and engineering and form the basis for the mathematical modeling of many physical systems. Their theoretical and numerical analysis thus plays an important role in applied mathematics and applications. Hyperbolic conservation laws present unique challenges for both theory and numerics as smoothness of their solution breaks down and produce discontinuities. The main aim of this workshop is to introduce this area to the young researchers starting from the basics to the advanced level from theoretical as well as computational point of view so that they can take up this area for their further research.
|
Name of the Speakers |
Affiliation |
No. of Lectures |
Detailed Syllabus |
|
Veerappa Gowda
|
TIFR-CAM,Bangalore |
4 lectures of one and half hours and one tutorial |
Scalar conservation laws and Hamilton-Jacobi equations: Hamilton-Jacobi equations,Legendre transform,Hopf-Lax formula, viscosity solutions. Lax-Oleinik formula for the solution of convex conservation laws and its long time behaviour. |
|
Adimurthi
|
TIFR-CAM,Bangalore |
4 lectures of one and half hours and one tutorial |
Conservation laws: weak solutions, entropy conditions, the viscous problem, Existence of an Entropy solution for scalar conservation laws. Uniqueness result. |
|
K T Joseph
|
TIFR-CAM,Bangalore |
4 lectures of one and half hours |
Systems of Conservation laws: Introduction to Riemann problem, Shocks and rarefaction, Entropy condition,General existence and uniqueness result for the Riemann problem for systems with the characteristics fields which are either linearly degenerate or genuinely nonlinear. Example: the p-system. Some results on different regularizations of the system, admissibility of discontinuous solutions and entropy conditions. |
|
Harish Kumar
|
IIT-Delhi |
3 lectures of one and half hours and two tutorials |
Numerical approximation of scalar conservation laws: Consistency,stability and Lax-Wendroff theorem. Monotone schemes, Godunov, Enquist-Osher and Lax-Friedrichs schemes. Convergence of monotone schemes to entropy solutions. TVD schemes. |
|
C Praveen |
TIFR-CAM,Bangalore |
3 lectures of one and half hours and two tutorials |
Discontinuous Galerkin method for scalar and system of conservation laws: basis functions, energy and entropy stability, TVD property and limiters, maximum principle satisfying schemes, time integration, numerical implementation |
References:
1. Partial Differerential equations by L C Evans
2. Hyperbolic system of conservation laws by E Godlewski and P A Raviart, Vol I & II
3. Numerical methods for conservation laws by Leveque
4. Shock Waves and Reaction Diffusion Equations by J. Smoller
Tentative time-table mentioning the names of speakers with their affiliation:
|
Day |
Date |
Speaker 1 (9.30–11.00) |
Tea (11.00–11.30) |
Speaker 2 (11.30–1.00) |
Lunch (1.00–2.00) |
Speaker 3 (2.00–3.30) |
Tea (3.30-4.00) |
Discussion (4.00-5.00) |
Snacks 5.00-5.30 |
|
|
|
(name of the speaker 1 |
|
(name of the speaker 2 |
|
(name of the speaker 3 |
|
(Name of the tutor) |
|
|
Mon |
01-02-2016 |
VG |
- |
ADI |
- |
VG |
- |
ADI |
- |
|
Tues |
02-02-2016 |
ADI |
- |
VG |
- |
ADI |
- |
VG |
- |
|
Wed |
03-02-2016 |
VG |
- |
HK |
- |
ADI |
- |
HK |
- |
|
Thu |
04-02-2016 |
KTJ |
- |
HK |
- |
CP |
- |
HK |
- |
|
Fri |
05-02-2016 |
CP |
- |
KTJ |
- |
HK |
- |
CP |
- |
|
Sat |
06-02-2016 |
KTJ |
- |
CP |
- |
KTJ |
- |
CP |
- |
- ADI-Adimurthi,TIFR-CAM,Bangalore
- CP- C Praveen, TIFR-CAM,Bangalore
- KTJ-K T Joseph,TIFR-CAM,Bangalore
- HK- Harish Kumar, IIT-Delhi
- VG-Veerappa Gowda,TIFR-CAM,Bangalore