Research

Journal Articles

• 1. Pradipta Chatterjee, Venkateswaran P. Krishnan and Abhilash Tushir. Inversion of spherical mean transform in odd dimensions with partial data via system of ODEs. (Accepted for publication)
     Analysis and Mathematical Physics
     http://arxiv.org/abs/2601.17411

  2. Aparajita Dasgupta, Shyam Swarup Mondal, Michael Ruzhansky, Abhilash Tushir.  Discrete time-dependent wave equation for the Schrödinger operator with unbounded potential, 563(2,Part 1):130762, (2026)
     Journal of Mathematical Analysis and Applications
     https://doi.org/10.1016/j.jmaa.2026.130762

  3. Aparajita Dasgupta, Michael Ruzhansky, Abhilash Tushir. Global well-posedness of space-time fractional diffusion equation with Rockland operator on graded Lie group.
     Mathematical Methods in the Applied Sciences, 48 , 4904–4923, (2025)
     http://doi.org/10.1002/mma.10583

  4. Aparajita Dasgupta, Shyam Swarup Mondal, Michael Ruzhansky, Abhilash Tushir. Time-fractional discrete diffusion equation for Schrödinger operator.
     Fractional calculus and applied analysis, 27, 3208–3239 (2024).
     https://doi.org/10.1007/s13540-024-00323-y

  5. Marianna Chatzakou, Aparajita Dasgupta, Michael Ruzhansky, Abhilash Tushir.  Discrete heat equation with irregular thermal conductivity and tempered distributional data.
     Proceedings of the Royal Society of Edinburgh Section A: Mathematics, (2025); 155(1): 57-80. (Open access) https://doi.org/10.1017/prm.2023.84

  6. Aparajita Dasgupta, Michael Ruzhansky, Abhilash Tushir. Discrete Time-Dependent Wave Equations II. Semiclassical Fractional Klein-Gordon Equation.
     Aequationes Mathematicae,  99, 1491–1505 (2025).
     https://doi.org/10.1007/s00010-025-01164-7

  7.  Aparajita Dasgupta, Michael Ruzhansky, Abhilash Tushir, Discrete time-dependent wave equations I. Semiclassical analysis.
     Journal of Differential Equations 317, 89–120 (2022).
     https://doi.org/10.1016/j.jde.2022.01.048 

Book Chapters

• 8. Marianna Chatzakou and Abhilash Tushir, Chapter: Very weak solution of the discrete heat equation with irregular time-dependent thermal conductivity.  Inbook: Ruzhansky, M., Torebek, B. (eds) Extended Abstracts MWCAPDE 2023. MWCAPDE 2023. Trends in Mathematics, vol 1. Birkhäuser, Cham (2024). https://doi.org/10.1007/978-3-031-41665-1_14

  9. Shyam Swarup Mondal and Abhilash Tushir, Chapter: Very Weak Solution of the discrete wave equation for Harmonic Oscillator Inbook: Ruzhansky, M., Van Bockstal, K. (eds) Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics, vol 2. Birkhäuser, Cham (2024). https://doi.org/10.1007/978-3-031-42539-4_27

Preprints

• 10. Aparajita Dasgupta, Shyam Swarup Mondal, Abhilash Tushir.  Fractional semilinear  damped wave equation on the Heisenberg group.
      https://arxiv.org/pdf/2501.10816

  11. Aparajita Dasgupta, Lalit Mohan, Abhilash Tushir. Structurally damped semilinear evolution equation for positive operators on Hilbert space.
      http://arxiv.org/abs/2507.14581

  12. Pradipta Chatterjee, Nisha Singhal and Abhilash Tushir. A Unified Range Characterization for the Spherical mean transform.
      https://arxiv.org/abs/2605.27034

Research Collaborators

1. Aparajita Dasgupta, IIT Delhi, (Ph.D Supervisor)

2. Michael Ruzhansky, Ghent University, Belgium (Ph.D Supervisor)

3. Marianna Chatzakou, Ghent University, Belgium 

4. Lalit Mohan, IIT Delhi

5. Shyam Swarup Mondal, ISI Kolkata

6. Venkateswaran P. Krishnan, TIFR Cam, Bangalore (Post Doc Mentor)

7. Pradipta Chatterjee, TIFR Cam, Bangalore

8. Nisha Singhal, TIFR Cam, Bangalore