Finite Element Analysis of a Nonlinear Predator-Prey System with Robin Boundary Conditions

     A convex open boundary domain was used to define the predator-prey equations. This was then mathematically analysed using Robin boundary conditions. Using the Faedo-Galerkin methodology and compactness arguments, we demonstrate the existence of strong and weak solutions and their uniqueness. The solution findings exhibit a higher level of regularity. We construct a more regular model based on the initial data. Furthermore, we can demonstrate continuous dependence on initial conditions. To complement the theoretical results, numerical simulations were also conducted, confirming the validity of the model and illustrating the dynamic behaviour of the predator-prey system under Robin boundary conditions.