Research interests

Partial Integro-Differential Equations: Coagulation-Fragmenation Models, Well-posedness, Regularity, Mass-conservation, Gelation, Large time behaviour, Stationary solutions, Self-similar profiles, Numerical Methods, Error Analysis
Stochastic Partial Differential Equations: Well-posedness, Regularity and Convergence Analysis of Numerical Methods
Inverse Problems: Variational Regularization and Iterative Regularization, Sotchastic methods, Stability Estimates, Regularized Solutions, Convergence, Convergence Rates, Mathematical imaging

Research Group:

Current Ph.D. Students:
Ikjot Kaur Mathematical analysis for Coagulation-annihilation models
Harshit Bajpai Fast and efficient iterative methods for solving nonlinear inverse problems
Simran Soni Stochastic differential equations
Ravi Verma Nonlinear Analysis with applications

Former Ph.D. Students:
Dr. Prasanta Kumar Barik Nonsingular and Singular Coagulation Models with Linear and Nonlinear Breakage
(Currently working as Assistant Professor, BITS Pilani, Dubai Campus, UAE) (Thesis Defended on 14/09/2018)
Dr. Vivek Kumar On Well-Posedness for Generalized Stochastic Burgers-Type Equations
(Currently working as Postdoctoral fellow at ISI-Bangalore) (Thesis Defended on 12/06/2019)
Dr. Gaurav Mittal Regularization for Nonlinear Inverse Problems via Stability Constraints
(Currently working as Scientist-C in DRDO, New Delhi) (Thesis Defended on 02/05/2022)
Dr. Pooja rai Oort-Hulst-Safronov coagulation model and its discrete counterpart with singular and nonsingluar unbounded coefficients (Currently working as Assistant Professor in VVPG College, Shamli, U.P.) (Thesis Defended on 10/08/2022)
Dr. Mashkoor Ali Mathematical Theorey on the Discrete Collision-induced Breakage Equations and the Safronov- Dubovskii coagulation Equations (Currently working as Assistant Professor in O. P. Jindal Global University, Sonipat) (Thesis Defended on 05/10/2023)
Dr. Pratibha Verma The Discrete and Continuous Redner-Ben-Avraham-Kahng Coagulation Models: Well-posedness, Large Time Behaviour an Their Connection, (Currently working as Domain Expert in Turing IN)(Thesis Defended on 11/07/2024)
Dr. Ram Gopal Jaiswal On the well-posedness and self-similarity of continuous nonlinear fragmentation models (Thesis Defended on 12/06/2025)
Saroj Si Growth-coagulation-fragmentation models: well-posedness, gelation and asymptotic behavior (Thesis Submitted)

Publications:

  1. Convergence Analysis of Kaczmarz-type iteratively regularized Landweber iteration for solving ill-posed inverse problems, Journal of Complexity, Accepted for Publication (with G. Mittal and H. Bajpai)
  2. Mass-conserving self-similar solutions to collision-induced breakage equations, SIAM J. Math. Anal., 57, 4, 3695-3717, 2025 (with R. G. Jaiswal)
  3. Mass-conserving weak solutions to the continuous nonlinear fragmentation equation in the presence of mass transfer, Nonlinear Analysis: Real World Applications, 85, 104381, 2025 (with R. G. Jaiswal)
  4. Well-posedness of the growth-coagulation equation with singular kernels, Nonlinear Analysis: Real World Applications, 84, 104300, 2025 (with Ph. Laurencot and S. Si)
  5. A note on the mixed discrete-continuous coagulation-fragmentation equation, Z. Angew. Math. Phys. (ZAMP), 76, 78, 2025 ( with M. Ali and P.K. Barik)
  6. Stochastic Data-Driven Bouligand Landweber Method for Solving Non-smooth Inverse Problems, J. Inverse and Ill-posed Problems, https://doi.org/10.1515/jiip-2024-0012, 2025(with H. Bajpai and G. Mittal)
  7. A novel two-point Landweber-type method for regularization of non-smooth inverse problems in Banach spaces, Computational and Applied Mathematics, 43, 426, 2024 (with G. Mittal and H. Bajpai)
  8. Convergence analysis of iteratively regularized Landweber iteration with uniformly convex constraints in Banach spaces, Journal of Complexity, 86, 101897, 2025 (with G. Mittal and H. Bajpai)
  9. The continuous collision-induced nonlinear fragmentation equation with non-integrable fragment daughter distributions, Journal of Differential Equations, 403, 235-271,2024 (with R. G. Jaiswal and Ph. Laurencot)
  10. A note on the Discrete Coagulation Equations with Collisional Breakage, Acta Applicandae Mathematicae, 189, 5, 2024 (with M. Ali)
  11. The discrete collision-induced breakage equation with mass transfer: well-posedness and stationary solutions, SIAM J. Math. Anal., 56 (3), 2915-2937, 2024 (with M. Ali and Ph. Laurencot)
  12. On the discrete Safronov-Dubovskiǐ coagulation equations: well-posedness, mass-conservation and asymptotic behaviour, Math. Meth. Appl. Sci. 47(6), 5191-5206, 2024 (with M. Ali and P. Rai)
  13. Well-posedness of the discrete collision-induced breakage equation with unbounded fragment distribution, Nonlinear Analysis: Real World Applications, 75, 103967, 2024 (with M. Ali and Ph. Laurencot)
  14. A modified iteratively regularized Landweber iteration method: Holder stability and convergence rates, J. Inverse and Ill-posed Problems, 32(6), 1141-1159, 2024(with G. Mittal)
  15. Convergence analysis of inexact Newton-Landweber iteration with frozen derivative in Banach spaces, J. Inverse and Ill-posed Problems, 32 (3), 497-511, 2024(with G. Mittal)
  16. Numerical study of finite volume scheme for coagulation-fragmentation equations with singular rates, Journal of Hyperbolic Differential Equations, 20 (4), 793-823, 2023 (with S. K. Bariwal, P. K. Barik and R. Kumar)
  17. The continuous Redner-Ben-Avraham-Kahng coagulation system: well-posedness and asymptotic behaviour, Evolution Equations and Control Theory, 12(5), 1247-1267, 2023 (with P. Verma, F. da Costa)
  18. Instantaneous gelation and nonexistence of weak solutions for the Oort-Hulst-Safronov coagulation model, Proceedings of Royal Society London A, 479, 20220385, 2023 (with P. Rai, V. John)
  19. A modified steepest descent method for solving non-smooth inverse problems, Journal of Computational and Applied Mathematics, 424, 114997, 2023 (with G. Mittal)
  20. Improved local convergence analysis of Landweber iteration in Banach spaces, Archiv der Mathematik, 120, 195–202, 2023 (with G. Mittal)
  21. Nonstationary iterated Tikhonov regularization: Convergence analysis via Hölder stability, Inverse Problems, 38, 125008, 2022 (with G. Mittal)
  22. Global existence of solutions to the discrete Safronov–Dubovskii coagulation equations and failure of mass-conservation, J. Math. Anal. Appl, 519(1), 126755, 2023 (with M. Ali)
  23. Convergence Analysis of an optimally accurate frozen Multi-Level projected steepest descent Iteration for solving inverse problems, J. Complexity, 101711, 2022 (with G. Mittal)
  24. Convergence Analysis of iteratively regularized Gauss-Newton method with frozen derivative in Banach spaces, J. Inverse and Ill-posed Problems, 30(6), 857-876, 2022 (with G. Mittal)
  25. Novel multi-level projected iteration to solve inverse problems with nearly optimal accuracy, J. Optim. Theory Appl., 194:643–680, 2022 (with G. Mittal)
  26. Mass-conserving weak solutions to Oort-Hulst-Safronov coagulation equation with singular rates, Journal of Differential Equations, 326, 164--200, 2022 (with P.K. Barik, P. Rai)
  27. On a generalized stochastic Burger's equation perturbed by Volterra noise, J. Math. Anal. Appl., 506(1), Article No. 125638, 2022 (with V. Kumar, M.T. Mohan)
  28. Convergence rates for iteratively regularized Gauss-Newton method subject to stability constraints, J. Comput. Appl. Math., 400, Article No. 113744, 2022(with G. Mittal)
  29. A novel two-point gradient method for regularization of inverse problems in Banach spaces, Applicable Analysis, 101 (18), 6596-6622, 2022 (with G. Mittal)
  30. Existence and non-existence for collision-induced breakage equation, SIAM J. Math. Anal., 53(4), 4605--4636, 2021 (with Ph. Laurencot)
  31. Existence and uniqueness of weak solutions to the singular coagulation equation with collisional breakage, NoDEA Nonlinear Differential Equations Appl., 28, Article No. 34, 2021(with P.K. Barik)
  32. Weak solutions to the collision-induced breakage equation with dominating coagulation, Journal of Differential Equations 288, 690-729, 2021 (with Ph. Laurencot)
  33. Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates, Kinetic and Related Models, 14(2):389-406, 2021 (with P.K. Barik, R. Kumar)
  34. Iteratively regularized Landweber iteration method: Convergence analysis via Holder Stability, Applied Mathematics and Computation, 392: Article No. 125744, 2021 (with G. Mittal)
  35. On a mixed fractional Burgers type equation with polynomial nonlinearity and perturbed by fractional Brownian sheet, Stochastic Analysis and Applications, 39(4), 610-630, 2021 (with V. Kumar)
  36. Weak solutions to the continuous coagulation model with collisional breakage, Discrete and Continuous Dynamical Systems-Series A, 40(11), 6115-6133, 2020 (with P.K. Barik)
  37. On Variational Regularization: Finite dimension and Holder stability, J. Inverse and Ill-posed Problems,29(2), 283-294, 2021(with G. Mittal)
  38. Global classical solutions to the continuous coagulation equation with collisional breakage, Z. Angew. Math. Phys. (ZAMP), 71, Article No. 38, 1-23, 2020 ( with P.K. Barik)
  39. Mass-Conserving solutions to the Smoluchowski coagulation equations with singular kernel, Proceedings of Royal Society Edinburgh, A 150(4), 1805-1825, 2020 ( with P.K. Barik and Ph. Laurençot)
  40. Generalized stochastic Burgers' equation with non-Lipschitz diffusion coefficient, Commun. Stoch. Anal., 12(3), 329-342, 2018 (with V. Kumar)
  41. A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation, Kinetic and Related Models, 11 (5), 1125-1138, 2018 (with P.K. Barik)
  42. Convergence of the cell average technique for Smoluchowski coagulation equation, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 49 (2), 349-372, 2015(with A.K. Nagar)
  43. On the uniqueness for coagulation and multiple fragmentation equation, Kinetic and Related Models (KRM), 6(3), 589-599, 2013
  44. Stochastic Burger's equation with polynomial nonlinearity driven by Levy process, Commun. Stoch. Anal. (COSA), 7(1), 91-112, 2013 (with E. Hausenblas)
  45. Convergence analysis of sectional methods for solving aggregation population balance equations: The fixed pivot technique, Nonlinear Analysis: Real World Applications, 14, 2068-2090, 2013 (with E. Hausenblas)
  46. Weak solutions to the continuous coagulation equation with multiple fragmentation, Nonlinear Analysis: Theory, Methods and Applications, 75, 2199-2208, 2012 (with Ph. Laurencot, and G. Warnecke)
  47. Uniqueness for coagulation-fragmentation equations with strong fragmentation, Z. Angew. Math. Phys. (ZAMP), 62, 1047-1063, 2011 (with G. Warnecke)
  48. The continuous coagulation equation with multiple fragmentation, J. Math. Anal. Appl., 374: 71-87, 2011 (with J. Kumar and G. Warnecke)

Collaborators:

  • Prof. Philippe Laurencot (CRNS, University of Toulouse, France)

  • Prof. Volker John (Weierstass Institute for Applied Analysis and Stochastics and Freie Unversity Berlin, Germany)

  • Prof. Otmar Scherzer (Radon Institute for Computational and Applied Mathematics (RICAM) Linz and University of Vienna, Austria)

  • Prof. Erika Hausenblas (University of Leoben, Austria)

  • Prof. Gerald Warnecke (University of Magdeburg, Germany)

  • Prof. Fernando da Costa (IST Lisbon and University of Aberta Lisbon, Portugal)

  • Prof. Michael Grinfeld (University of Strathclyde, Glasgow, UK)

  • Prof. Youcef Mammeri (University of Picardie Jules Verne, Amiens, France)

  • Prof. Joaquim Correia (University of Evora, Portugal)

  • Prof. Nabil Badjaoui (University of Picardie Jules Verne, Amiens, France)

  • Prof. Marilia Pires (University of Evora, Portugal)

  • Prof. Jacek Banasiak (University of Pretoria, South Africa)

    • Scientific Research Projects:

    • "Fast and computationally efficient iterative regularization methods for solving inverse problems, Core Research Grant, SERB, New Delhi, Approved.

    • "The discrete coagulation equations with collisional breakage", MATRICS, SERB, New Delhi, Approved.

    • Indo-French joint project on "Collision-induced Fragmentation and Coagulation: Dynamics and Numerics" funded by IFCAM (Indo-French Centre for Applied Mathematics), August 2019-March 2023. (with Prof. Philippe Laurencot, CNRS, University of Toulouse, France)

    • Indo-German joint project on "Analysis and Numerical Methods for Population Balance Equations" funded by DST-DAAD, July 2019-June 2021. (with Prof. Volker John, WIAS Berlin, Germany)

    • "Coagulation-fragmentation models: Well-posedness, Numerical approximations and Asymptotic analysis" funded by SERB, New Delhi, India, October 2016-October 2019.

    • Faculty Initiation Grant (FIG) funded by IIT Roorkee, September 2015-September 2018.