Research Overview
Research Overview
My area of interest primarily lies in mathematical analysis and numerical simulations of a system of partial differential equations describing ecological phenomenon. The system of partial differential equations that I primarily deal with are parabolic and are of the following type :
A suitable boundary condition is also imposed depending upon the situation. The major challenge in solving such problems is that the Laplacian operator acts over a nonlinear function making the analysis challenging. The analytical techniques that are employed by me to prove the existence of solutions for such type of systems are:
Degree Theory and Fixed point index based methods
Bifurcation Theory
Monotone Iterative Technique
The spatiotemporal models that I develop generally describe ecological phenomenon. Through application of competent analytical technique it is proved that the systems admits positive solutions indicating coexistence phenomenon of nature. Numerical simulations of such systems are then carried out to study the phenomenon of Pattern Formation commonly exhibited by such reaction diffusion systems.