Research interests

• Controllability and stabilization of coupled PDEs

• Control of fluid and fluid–structure interaction systems

• Geometric control theory and nonlinear PDEs

Methods and techniques: 

Backstepping, moment methods, Lebeau-Robbiano spectral approach, Carleman estimates, method of characteristics, multiplier methods, compactness–uniqueness arguments, Ingham-type inequalities, flatness methods, event-triggered control, source-term methods, Lyapunov estimates, Riccati-based feedback stabilization, Agrachev–Sarychev geometric control techniques.

Preprints

• Global controllability of the Cahn-Hilliard equation (with Víctor Hernández-Santamaría and Luz de Teresa).

• On the controllability of the Kuramoto-Sivashinsky equation in multi-dimensional cylindrical domains (with Víctor Hernández-Santamaría).

• Small-time global controllability of a class of bilinear fourth-order parabolic equations (with Debanjit Mondal).

• Local controllability of the Cahn-Hilliard-Burgers equation around certain steady states (with Manika Bag, Sheetal Dharmatti and Debanjana Mitra).

Publications

• A Hierarchical control problem for the Benney-Lin equation using Stackelberg-Nash strategy, Appl. Math. Optim., 93 (2026), pp. 1–64 (with Manish Kumar).

• Boundary null controllability of a class of 2-D degenerate parabolic PDEs, Discrete Contin. Dyn. Syst., 45 (2025), pp. 5107–5153 (with Víctor Hernández-Santamaría and Luz de Teresa).

• Event-triggered boundary control of the linearized FitzHugh-Nagumo equation, Automatica J. IFAC, 179 (2025), pp. 1–15 (with Víctor Hernández-Santamaría and Luz de Teresa).

• Insensitizing control problem for the Kawahara equation, NoDEA Nonlinear Differential Equations Appl., 32 (2025), pp. 1–38 (with Manish Kumar).

• Stabilization of Kawahara equation with saturated internal or boundary feedback controls, Math. Control Relat. Fields, 15 (2025), pp. 845–875 (with Hugo Parada).

• Controllability and Stabilizability of the linearized compressible Navier-Stokes system with Maxwell's law, J. Evol. Equ., 25 (2025), pp.1–60 (with Sakil Ahamed).

• On the controllability of a system coupling Kuramoto-Sivashinsky-Korteweg-de Vries and transport equations, Math. Control Signals Systems, 36 (2024), pp. 875–926 (with Manish Kumar).

• Coupled linear Schrödinger equations: Control and stabilization results, Z. Angew. Math. Phys., 75 (2024), pp. 1–31 (with Kuntal Bhandari, Roberto de A. Capistrano-Filho and Thiago Yukio Tanaka).

• Local exponential stabilization of Rogers-McCulloch and FitzHugh-Nagumo equations by the method of backstepping, ESAIM Control Optim. Calc. Var., 30 (2024), pp. 1–45, (with Shirshendu Chowdhury and Rajib Dutta).

• Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a single Neumann control, Evol. Equ. Control Theory, 13 (2024), pp. 587–615 (with Kuntal Bhandari and Jiten Kumbhakar).

• Local null controllability of the stabilized Kuramoto-Sivashinsky system using moment method, Adv. Differential Equations, 29 (2024), pp. 223–290 (with Manish Kumar).

• Asymptotic behavior of the linearized compressible barotropic Navier-Stokes system with a time varying delay term in the boundary or internal feedback, Math. Meth. Appl. Sci., 46 (2023), pp. 17288–17312.

• Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations, J. Math. Anal. Appl., 525 (2023), pp. 1–33, 127213 (with Kuntal Bhandari).

• Boundary controllability and stabilizability of a coupled first-order hyperbolic-elliptic system, Evol. Equ. Control Theory, 12 (2023), pp. 907–943 (with Shirshendu Chowdhury and Rajib Dutta).

• Boundary stabilizability of the linearized compressible Navier-Stokes equation in one dimension by backstepping approach, SIAM J. Control Optim., 59 (2021), pp. 2147–2173 (with Shirshendu Chowdhury and Rajib Dutta).