NIT Jalandhar

डा बी आर अम्बेडकर राष्ट्रीय प्रौद्योगिकी संस्थान, जालंधर
Dr B R Ambedkar National Institute of Technology, Jalandhar

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Dr Mohammad Zafar

Name : Dr Mohammad Zafar
Designation : Assistant Professor (Grade-I)
Department : Mathematics
Qualification : Ph.D. Mathematics (IIT Bombay)
M.Sc. Mathematics (Kumaun University, Nainital)
B.Sc. Mathematics, Physics, Chemistry (Kumaun University, Nainital)
Address : Department of Mathematics, Dr B R Ambedkar NIT Jalandhar

Jalandhar (Punjab) - 144027
Phone : 0181-5037700 (Extn: 3010)
Email ID : zafarm@nitj.ac.in
Fax :

Other Profile Links

Personal Web Link : My web page
Google Scholar Link : M. Zafar

Research Profile

Research Interests : Quasilinear Systems of Partial Differential Equations; Hyperbolic Conservation Laws and Nonlinear Waves
Brief Research Profile: : Nonlinear (or quasilinear) hyperbolic system of partial differential equations, unlike their linear counterparts, come to us in tremendous variety; each with its own difficulties and require special treatments for solutions. The familiar laws of superposition, reflection, and refraction, applicable for linear partial differential equations, cease to be valid in case of nonlinear hyperbolic partial differential equations. The main complexity in the nonlinear hyperbolic partial differential equations is the break down of solutions within a finite span of time due to blow up of their derivatives and consequently forbidding the existence of global classical solutions. A fascinating feature appears in nature due to the breaking of solutions, i.e., the appearance of shock waves across which the medium undergoes abrupt changes in velocity, pressure and temperature. In contrast to the linear partial differential equations where signals propagate along the characteristics, the characteristics can cross each other precipitating the onset of a shock for nonlinear hyperbolic partial differential equations. An interesting example is the supersonic boom produced by an airplane that breaks the sound barrier. Indeed, a shock is an admissible discontinuity which satisfies Rankine-Hugoniot jump conditions and the entropy condition.

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Journal Publications

Year Journal Publication
2022 Mathematical Methods in the Applied Sciences (Wiley) H. Srivastava and M. Zafar, Three pieces Riemann problem for 2‐D full Euler system in the Noble–Abel gas
2022 Journal of Mathematical Physics (AIP, USA) Priyanka and M. Zafar, Delta Shocks and vacuum states in the Riemann solutions of Chaplygin Euler equations as pressure and magnetic field drop to zero
2018 Nonlinear Analysis: Real World Applications (Elsevier) M. Zafar and V. D. Sharma, Classification of the Riemann problem for compressible two-dimensional Euler system in non-ideal gas
2016 Nonlinear Analysis: Real World Applications (Elsevier) M. Zafar and V. D. Sharma, Expansion of a wedge of non-ideal gas into vacuum
2016 International Journal of Non-Linear Mechanics (Elsevier) M. Zafar, A note on characteristic decomposition for two-dimensional Euler system in van der Waals fluids
2014 Journal of Mathematical Physics (AIP, USA) M. Zafar and V. D. Sharma, Characteristic decomposition of compressible Euler equations for a non-ideal gas in two-dimensions

Conference Publications

Year Conference Publication

Book/Chapter Publications

Type Title Publisher Authors ISBN/ISSN No. Year

Research Projects

Role Project Type Title Funding Agency From To Amount Status Co-Investigator
Principal Investigator Existence of global classical solution to the interaction of bi-symmetric four planar rarefaction waves The National Board for Higher Mathematics (Govt. of India) 08-07-2021 07-07-2024 17.50 Lakhs Ongoing NIL

Events Organized

Category Type Title Venue From To Designation
STC International Numerical Solutions of Differential Equations NIT Jalandhar 16-09-2020 20-09-2020 Co-ordinator

Professional Affilation

Designation Organization
Life Member Indian Mathematical Society
Life Member Ramanujan Mathematical Society
Life Member Indian Society of Theoretical and Applied Mechanics

PhD Supervised

Scholar Name Research Topic Status Year Co-Supervisor
Priyanka Certain aspects of delta-shock waves Ongoing NIL
Shailee Sharma Ongoing NIL
Harsita Srivastava A Study on Two-Dimensional Riemann Problems for Conservation Laws Ongoing NIL

PG Dissertation Guided

Student Name Dissertation Title Status Year Co-Supervisor

Patents

Name Reg./Ref. No. Date of Award/Filling Organization Status

Admin. Responsiblities

Position Held Organization From To

Award and Honours

Title Activity Given by Year