Research Projects

Inverse problems have strong impact on numerous disciplines leading to enormous applications. Classical research in inverse problems involve fusion of mathematical modeling of the system followed by analysis, further we progress by creating a suitable algorithm to the model. Finally, implementation of the findings and validation of the results is carried out. Our aim is to study both the theoretical and numerical version of the inverse problem by reconstructing the time/space dependent source/coefficient in the biological models from the given output measured data. Initially, the existence and uniqueness of an inverse problem is obtained under certain assumptions on the input data using Schauder's fixed point theorem. In order to find the unknown source/coefficient term approximately, we establish a time-discretized system. Further we progress by analysing the existence, uniqueness for time-discretized system and the convergence rates for both exact and noisy data. Finally, the solution of inverse problems and theoretical convergence rate results are verified through suitable numerical illustrations. In this project, we will study the following list of problems: 1. Inverse source problems for Brain Tumor Model. 2. Inverse source problems for Phase-field Tumor Growth Model 3. Coefficient inverse problems of reconstructing the time dependent external signal production rate in Cattaneo Chemotaxis Model. 4. Inverse source problems for coupled system of partial differential equations arising in Biological Pattern Formation