Name: Dr. N. Barani Balan Designation: Assistant Professor Phone: 04366-277230 Email:baranibalan@cutn.ac.in
Biographic Sketch:
I am an Assistant Professor of Mathematics at School of Mathematics & Computer Sciences, Central University of Tamil Nadu (CUTN), Thiruvarur, Tamil Nadu.
I graduated with M.Sc., M.Phil. in Mathematics from Bharathiar University (BU) and under graduation from Periyar University, Salem. I received my PhD (Mathematics) from BU, Coimbatore. Initially, I worked as guest faculty for few years in my parent institution. Three years later it was time to move on, as I was selected for a temporary position followed by a permanent one at CUTN and am working here thereafter.
My research work is based on Partial Differential Equations and its applications to Control and Inverse Problems which is a highly substantial field in Mathematics. I have consistent growth in my research which depicts through my projects and papers. I share my ideas with other esteemed researchers and perform collaborative research in various fields both within and outside India. I have conducted workshops and conferences at our University in association with other central and state Institutions. My flexibility supports me in the classroom, where there are many different personalities and learning styles. My experience with eminent teachers has given me the perspective to present quality teaching and has strengthened my potentiality. I take the responsibilities given to me effectively and execute the best. I strongly believe that integrity lies in being true to ourselves
Research Highlights :
I chose to work in Inverse Problems (IP) as it is cross-disciplinary within mathematics and across disciplines, including physical sciences, engineering and biology. Thus, it allows me to apply beautiful and deep mathematics to problems with social and environmental impact. The objectives are to investigate the existence, uniqueness and stability of the solution to the problem that mathematically models a physical phenomenon under investigation, and to develop new convergent and stable algorithms for obtaining the desired solution.
Present Investigation Zone:
Inverse coefficient problems with boundary data for parabolic partial differential equations and systems using Carleman technique.
Source identification problems for linear/non-linear parabolic systems. Developing the numerical methods based on adjoint formulations.
Reconstruction of sources and leading coefficients of parabolic systems by using adjoint and Quasi-solution method.
Simultaneous identification of coefficients in the parabolic systems by using optimization technique.
Theoretical and Numerical optimal control problems for Parabolic Partial Differential Equations.
I am planning to explore my ideas in novel areas of research which includes Fractional Optimization Method and Inverse Problems for Fractional Partial Differential Equations.
Recent Publications :
1. Identification of Source Terms in a Coupled Age-Structured Population Model with Discontinuous Diffusion Coefficients, AIMS Mathematics, 2 (2017) 81-95 (with V. Dinakar and K. Balachandran)
2. Inverse Problems for Parabolic Equation with discontinuous Coefficients, Nonautonomous Dynamical System, 4 (2017) 40-51 (with V. Dinakar and K. Balachandran)
3. Inverse Problems and Trajectory Controllability for the Swift-hohenberg Equation, Indian Journal of Industrial and Applied Mathematics, 10(2) (2019) 253- 269 (with A. Arivazhagan)
4. Lipschitz Stability of an Inverse Problem for the Kawahara Equation with Damping, AIMS Mathematics, 5 (2020), 4529-4545 (with A.Arivazhagan and K. Sakthivel)
5. Inverse Problems for a Cahn-Hilliard Type System Modelling Tumor Growth, Applicable Analysis 101 (2022) 858-890 (with A.Arivazhagan and K. Sakthivel)
6. Inverse Source Problem for the Generalized Korteweg-de Vries Equation, Journal of Inverse and Ill-Posed Problems 29 (2021) 823-848. (with A.Arivazhagan and K. Sakthivel)
7. Analyzing Lotka Volterra Reaction-Diffusion Model Using Optimization Technique, Indian Journal of Industrial and Applied Mathematics, 11 (2020) 174-192 (with K. Navaneetha Krishnan, S. Hemalatha, L. Shangerganesh)
8. An Optimal Control Problem for Acid-mediated Cancer Invasion Model, Journal of Applied Nonlinear Dynamics 12(2) (2023) 339-351 (with M. Navaneetha Krishnan, L. Shangerganesh and J. Manimaran)
9. Blow-up Phenomena for a sixth-order partial differential equation with a general non-linearity, Journal of Dynamical and Control Systems (accepted) (with A. Arivazhagan, L. Shangerganesh, K. Dravid)
10. Prey-Predator model with an infection in both population: Stability analysis and an optimal control study, Discontinuity, Nonlinearity and complexity (with S. Hariharan, K.P. Sreesiva, L. Shangerganesh
