Dr. Rakib Mondal

Short Bio

Welcome to the personal homepage of Dr. Rakib Mondal. He is a Postdoctoral researcher in the Department of Mathematics, IIT Bombay, working in the area of partial differential equations, hyperbolic systems, and nonlinear conservation laws. Before this, he was a postdoctoral researcher in the Department of Mathematics, IIT Kharagpur. He earned his Ph.D. in Mathematics, where his research focused on the global existence, stability, and qualitative behavior of solutions to nonlinear systems of conservation/balance laws. His research interests include the analysis of nonlinear PDEs, hyperbolic conservation laws, Riemann problems, Cauchy problems, measure solutions, and shock waves. He is particularly interested in developing rigorous analytical techniques to study nonlinear wave propagation and complex phenomena arising in fluid dynamics and continuum mechanics. His work involves tools and methods such as asymptotic analysis, the weak convergence method, the nonlinear viscosity approximations, regularization methods, flux perturbation, compensated compactness techniques, and front tracking method, etc. He is interested in both the theoretical aspects of nonlinear PDEs and their applications to mathematical models arising in numerous physical problems in science and engineering. He is further interested in developing original ideas and novel techniques to investigate new problems in his research program. Moreover, beyond his research, he is interested in exploring new mathematical problems, collaborating with researchers from different areas, and contributing to the development of mathematical analysis of nonlinear phenomena.

Profile Links:

Google Scholar; ORCID; ResearchGate

Email:

Curriculum Vitae (PDF)

Research Interests

• Hyperbolic systems of conservation/balance laws
• Nonlinear partial differential equations
• Riemann and Cauchy problems
• Wave interactions and singular solutions
• Shock wave, Delta shock wave
• Mathematical models in fluid dynamics

Publications

• Rakib Mondal, Minhajul, Dia Zeidan, Delta shock interactions and stability of the Riemann solutions in generalized Chaplygin gas with time-dependent general source term, Journal of Mathematical Physics (American Institute of Physics), 67 (2026), 081502. DOI:10.1063/5.0311936.
• Richard De la cruz, Rakib Mondal, Wladimir Neves, Riemann problem for the chromatography-type system of Langmuir isotherm with source term, Nonlinear Analysis: Real World Applications (Elsevier), 93 (2026), 104673. DOI:10.1016/j.nonrwa.2026.104673.
• Rakib Mondal, Minhajul, Limiting behavior of Riemann solutions and formation of delta shock wave in the extended Chaplygin gas with Coulomb-type friction, Communications in Nonlinear Science and Numerical Simulation (Elsevier), 154 (2026), 109559. DOI:110.1016/j.cnsns.2025.109559.
• Rakib Mondal, Minhajul, Rarefaction wave interaction and existence of a global smooth solution in the blood flow model with time-dependent body force, Studies in Applied Mathematics (Wiley-MIT Press), 154 (2025), e70025. DOI:10.1111/sapm.70025.
• Rakib Mondal, Minhajul, Elementary wave interactions in two-layer blood flow model, Mathematical Methods in the Applied Sciences (Wiley), 48 (2025), 8778–8792. DOI:10.1002/mma.10752.
• Rakib Mondal, Minhajul, T. Raja Sekhar, Interactions between elementary waves and weak discontinuity in two-layer blood flow through artery, Physics of Fluids (American Institute of Physics), 36 (2024), 036121. DOI:10.1063/5.0199216.
• Rakib Mondal, Minhajul, On the interactions of arbitrary shocks in isentropic drift-flux model of two-phase flows, The European Physical Journal Plus (Springer), 139 (2024), 83. DOI:10.1140/epjp/s13360-024-04884-y.
• Minhajul, Rakib Mondal, Wave interaction in isothermal drift-flux model of two-phase flows, Chaos, Solitons & Fractals (Elsevier), 175 (2023), 114037. DOI:10.1016/j.chaos.2023.114037.
• Rakib Mondal, Minhajul, A Limiting Viscosity Approach to the Riemann Problem in Blood Flow Through Artery, Bulletin of the Malaysian Mathematical Sciences Society (Springer), 46 (2023), 184. DOI:10.1007/s40840-023-01579-y.

Preprints and Ongoing Work

• Preprints:
  • Richard De la cruz, Rakib Mondal, Wladimir Neves, Wave interactions and stability of Riemann solutions for a nonautonomous Chromatography-type system of Langmuir isotherm, arXiv:2607.29029 (2026). DOI:10.48550/arXiv.2607.29029.
• Ongoing work: To be updated.

Education

• Ph.D. in Mathematics, Birla Institute of Technology and Science, Pilani, India, 2026.
• M.Sc. in Pure Mathematics, University of Calcutta, Ballygunge, Kolkata, West Bengal, India, 2020.
• B.Sc. in Mathematics (Honours), University of Calcutta, Kolkata, West Bengal, India, 2017.

Conferences & Workshops

Conferences:

• Delivered a talk on "Existence and uniqueness of $C^1$ solution to the BVP for blood flow model with body forces" in The International Conference "Latest Advances in Computational and Applied Mathematics-2025 (LACAM-25)'' jointly organized by IISER Thiruvananthapuram, India, and University of Heidelberg, Germany, held from December 8 to 11, 2025.
• Delivered a talk on "Rarefaction wave interaction and existence of a global smooth solution in the blood flow model with time-dependent body force'' in "The Third Joint SIAM/CAIMS Annual Meetings (AN25) Virtual'' organized by Society for the Industrial and Applied Mathematics (SIAM), Montréal, Québec, Canada, held from July 28 to August 1, 2025.
• Delivered a talk on "Rarefaction Wave Interaction and Existence of a Global Smooth Solution for a hyperbolic system conservation laws with source" in the "15th International ISAAC Congress 2025" organized by Nazarbayev University, Astana, Kazakhstan, held from July 21 to July 25, 2025.
• Delivered a talk on "Interactions between elementary waves and weak discontinuity in the two-layer blood flow through arteries" in "The 19th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2024)" organized by Shanghai Jiao Tong University (SJTU), Shanghai, PR China, held from July 1 to July 5, 2024.
• Delivered a talk on "Elementary wave interactions with arbitrary strengths in two-layer blood flow through arteries" in "The 7th International Conference on Complex Dynamical Systems and Applications (CDSA 2024)" organized by Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India, held from January 25 to January 27, 2024.
• Delivered a talk on "On the interactions of arbitrary shocks in the drift-flux model of two-phase flows" in The Annual Conference "The Indian Women and Mathematics (IWM)" organized by Department of Mathematics, BITS Pilani, K K Birla Goa Campus, Goa, India, held from July 11-13, 2024.
• Delivered a talk on "On the interactions of elementary waves with a weak discontinuity in the two-layer blood flow model" in the "International Conference on Differential Equations and Control Problems (ICDECP23)" organized by the School of Mathematical & Statistical Sciences, Indian Institute of Technology Mandi, India, held June 15 to June 17, 2023.
• Participated in the "9th International Conference on Mathematics and Computing (ICMC 2023)" organized by Department of Mathematics, BITS Pilani, K K Birla Goa Campus, Goa, India, held from Jan 06-08, 2023.

Workshops: To be updated.

Awards

• Recipient of ICM 2026 Travel Support Program for Young Mathematicians to participate in the International Congress of Mathematicians (ICM) 2026, Philadelphia, Pennsylvania, USA.
• Recipient of SIAM Travel Awards to participate in the SIAM Conference on Analysis of Partial Differential Equations (PD25), 2025, Pittsburgh, Pennsylvania, U.S.
• Recipient of Travel Grants for Young Mathematicians to participate in the 15th International ISAAC Congress 2025, Astana, Kazakhstan.
• Receipient International Travel Support Scheme (ITS), from the Science & Engineering Research Board (SERB), Anusandhan National Research Foundation (ANRF), India to participate in The 19th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2024), PR China. File Number: ITS/2024/002264.
• Received Swami Vivekananda Merit Cum Means (SVMCM) Scholarship to pursue higher studies from the Government of West Bengal, India.

Teaching

As Teaching Assistant at BITS Pilani, Goa Campus

• Mathematics I (Multivariable Calculus)
• Mathematics II (Linear Algebra & Complex Analysis)
• Mathematics III (Differential Equations)
• Probability & Statistics

Softwares and Skills

• LaTeX
• Mathematica
• MATLAB
• C++
• Mathematical modeling
• Mathematical Analysis