About the Faculty

I did my doctoral degree on "Optimal Control Problems Involving Parabolic Differential and Parabolic Integro-Differential" Equations from the Department of Mathematics, Indian Institute of Technology, Mumbai, India, under the supervision of Prof. Mohan C. Joshi and Prof. Amiya K. Pani. I joined the Department of Mathematics, BITS-Pilani KK Birla Goa Campus in 2006. My research area is numerical analysis and optimal control theory.

As part of my research work, I am working on the optimal control problems for linear and nonlinear partial differential equations and their applications, emphasizing theory and computation. The concept of controllability denotes the ability to move a system around in its entire configuration space using only specific admissible manipulations. The time-optimal control problem involves finding control in an admissible set that minimizes the particular cost functional. These problems arise naturally in various areas of science and technology, such as controlling the heat in the electrically heated oven and reheating furnaces, controlling the crystal growth/dissolution in the chemical process, controlling the crystal growth/dissolution in the chemical process, control of the concentration of an activator in biochemistry, and optimal portfolio selection process in the financial market. The theory of optimal control is one of the significant application areas in mathematics today. From its early origin to meet the demands of the automatic control system design in engineering, it has grown steadily in scope and has spread to many unrelated distinct areas such as economics and bio-sciences. My Ph.D. thesis focused on the optimal control problems associated with the controllability of parabolic differential equations and parabolic integro-differential equations using semi-group theory. We also perform numerical experiments on the penalized optimal control problems for different target states or final states for various control problems. Presently, I am working in the following areas: 

• Numerical approximation of optimal control problems involves partial differential equations by the virtual element method (VEM), a recently developed technique.
• Application of optimal control theory in software reliability growth modelling.
• Studying the decay rates and developing stabilization of finite element approximation to weakly damped wave equation and extending the analysis to strongly damped wave equation.
• Developing physics-informed Galerkin neural networks for optimal control problems governed by elliptic and parabolic partial differential equations (PDEs).