Research publications 

• Localizing acoustic and electromagnetic waves in space and time, (with R. Griesmaier), Submitted for publication. [arXiv]

• Minnaert frequency and simultaneous reconstruction of the Density, Bulk and Source in the time-domain wave equation, (with M. Sini),

Archive for Rational Mechanics and Analysis, 249 (2025), article no. 48. [Journal] [arXiv]

• Extension problem for the fractional parabolic Lamé operator and unique continuation, (with A. Banerjee),

      Calculus of Variations and Partial Differential Equations, 63 (2024), no. 8, paper no. 203, 33 pp.  [Journal] [arXiv]

• The Calderón problem for space-time fractional parabolic operators with variable coefficients, (with A. Banerjee), 

      SIAM Journal on Mathematical Analysis, 56 (2024), no. 4 , 4759–4810.  [Journal] [arXiv] 

• Recovering both the wave speed and the source function in a time-domain wave equation by injecting contrasting droplets, (with M. Sini, and H. Wang),

      Discrete and Continuous Dynamical Systems. Series A, 44 (2024), no. 5 , 1446-1474.  [Journal] [arXiv] 

• Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients, (with V. P. Krishnan, and Rakesh),

      Journal of Differential Equations, 342 (2023), 622-665.  [Journal] [arXiv]

• Stability estimate for a partial data inverse problem for the convection-diffusion equation, (with M. Vashisth),

      Evolution Equations and Control Theory, 11 (2022), 1681-1699.  [Journal] [arXiv]

• Stability for a formally determined inverse problem for a hyperbolic PDE with space and time dependent coefficients, (with V. P. Krishnan, and Rakesh),

      SIAM Journal on Mathematical Analysis, 53 (2021), no. 6, 6822-6846.  [Journal] [arXiv]

• Stability estimates for the relativistic Schrödinger equation from partial boundary data,

      Inverse Problems, 37 (2021), no. 1, paper no. 015001, 25 pp.  [Journal] [arXiv]

• A uniqueness result for light ray transform on symmetric 2-tensor fields, (with V. P. Krishnan, and M. Vashisth),

      Journal of Fourier Analysis and Applications, 26 (2020), no. 3, paper no 40, 20 pp.  [Journal] [arXiv] 

Book chapter :

• Inverse Problems in Imaging Using Resonant Contrast Agents, (with A. Ghandriche, and M. Sini),

Inverse Problems for Mechanical Systems: Methods, Simulations and Experiments, Volume 618, Pages 195-246, 2025. [Journal]

A glimpse into my research

I studied stability aspects in the inverse problem of determining time-dependent lower-order perturbations appearing in various evolution equations, both in their formally determined and over-determined setups. A part of my earlier research work also focused on integral geometry problems related to the light-ray transform. Additionally, I am interested in the strong unique continuation principles for PDEs and their potential applications in the framework of nonlocal inverse problems.

Broadly, the study of inverse problems concerns extracting intrinsic properties of a medium from a set of boundary observations, where the medium (in general) is governed by a model based on some PDE. Applications of such analysis cover a wide range of areas, including radar, medical and geophysical imaging, the petroleum industry for oil prospection, communication theory, remote sensing, and nondestructive testing. In principle, the main difficulty lies in inverting a nonlinear map or the absence of data from some inaccessible parts of the boundary. One also considers issues regarding stable inversion, reconstruction algorithms, and the unique and stable determination using limited data. Techniques from functional analysis, harmonic analysis, differential geometry, complex analysis, and microlocal analysis are commonly employed to address these types of problems.

Collaborators

Here is an alphabetical listing of my collaborators :

• Agnid Banerjee (Arizona State University, USA)  

• Roland Griesmaier (Kalrsruhe Institute of Technology, Germany)     

• Venkateswaran P. Krishnan (TIFR-CAM, Bangalore, India)

• Rakesh (University of Delaware, USA) 

• Mourad Sini (RICAM, Austrian Academy of Sciences, Austria)

• Manmohan Vashisth (IIT Ropar, India)

• Haibing Wang (Southeast University, China)