AIS - Hyperbolic Conservation Laws (2024)

Speakers and Syllabus


Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus


T. Raja Shekhar

IIT Kharagpur


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


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


Vanishing viscosity method, notion of Kruzhkov entropy solutions, travelling waves for scalar conservation laws.

Manas Ranjan Sahoo

NISER Bhubaneswar


Wave front tracking method for scalar conservation laws and hyperbolic systems(with an emphasis on 2\times 2 system)

Anupam Pal Choudhury

NISER Bhubaneswar


Diperna’s measure valued solutions. Initial-boundary value problems for scalar conservation laws and first order hyperbolic systems.

Tanmay Sarkar

IIT Jammu


Numerical methods for hyperbolic conservation laws, Conservative methods, Lax-Wendroff theorem, Godunov’s method, Riemann’s solver and TVD methods.




  1. Shock Waves and Reaction-Diffusion Equations: Joel Smoller

  2. Hyperbolic Conservation laws in Continum Physics: Constantine M. Dafermos

  3. Hyperbolic Systems of Conservation laws: Philippe G. LeFloch

  4. Front Tracking for Hyperbolic Conservation Laws: Helge Holden and Nils Henrik Risebro

  5. Partial Differential Equation: Lawrence C. Evans

Tutorial Assistants:

S. No.




Abhishek Das

NISER, Bhubaneswar


Abhrojyoti Sen



Balakrishna Chhatria

IIT Kharagpur


Mukul Dwivedi

IIT Jammu


Anirban Das



Kanchan Dwivedi

NIT Warangal



Time Table

 Time-Table (with names of speakers and course associates/tutors):

Day Date Lecture 1&2
(11.00 – 11.25)
(12.30– 2.25)
Lecture 3&4
(2.30– 4.00)
Tea and Snacks
(4.00 - 4.25)
    (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










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