Research

The research activities at TIFR-CAM under this chair can be classified under the following three headings

Homogenization and inverse problems

1. Stability estimates for an inverse boundary value problem for the biharmonic operator with bounded potentials

2. An efficient numerical algorithm for the inversion of an integral transform arising in ultrasound imaging

3. Common Midpoint versus common offset acquisition geometry in seismic imaging

4. Polarization tensors via homogenization theory

5. Recovering 2nd order Isotropic perturbation of a biharmonic operator from full boundary data

6. Microlocal analysis of a restricted Doppler transform in n-dimensional Euclidean space

7. Inversion of a class of circular and elliptical Radon transforms

8. Determination of Lower Order Perturbations of the Polyharmonic Operator from Partial Boundary Data

9. A class of singular Fourier integral operators in synthetic aperture radar imaging, II. Transmitter and receiver at different speeds

10. Inversion of spherical Radon transform in a spherical shell

11. Inversion of restricted ray transforms of symmetric tensor fields in n-dimensional Euclidean space

12. Microlocal analysis of a restricted ray transform of symmetric m-tensor fields in n-dimensional Euclidean space

13. Numerical inversion of a class of broken ray transforms with partial radial data in a disc

Control and stabilization of complex systems

1. Null controllability of Compressible Navier-Stokes system in one dimension

2. Flow control of Navier-Stokes-Boussinesq model

3. Stabilization of 2-D Navier-Stokes equations for square cylinder in channel

4. Feedback stabilization Problems on tree-like structures

5. Approximate Controllability Results for viscoelastic flows

6. A Fokker-Planck approach to control collective motion

Numerical schemes for fluid flows

1. A second order well-balanced finite volume scheme for Euler equations with gravity: ideal gas model

2. A second order well-balanced finite volume scheme for Euler equations with gravity: general equation of state

3. Well-balanced discontinuous Galerkin method for Euler equations with gravity

4. Entropy stable finite volume scheme for ideal MHD

5. Entropy stable discontinuous galerkin scheme for ideal compressible MHD equations

6. Entropy stable schemes on two-dimensional unstructured grids

7. An entropy stable discretization for the two dimensional Navier-Stokes equations with stable boundary treatment

8. A sign preserving WENO reconstruction

9. Discontinuous Galerkin scheme for Euler and MHD equations on adaptive meshes

10. Positivity preserving Discontinuous Galerkin scheme for ideal MHD

11. An arbitrary Lagrangian-Eulerian discontinuous Galerkin method for compressible flows