A diffusive predator-prey system with a free boundary

In this paper, we consider a problem with a free boundary for a diffusive predator-prey system in the onedimensional case. Nonlinear problems with free boundary are studied using a method based on constructing a priori estimates. Therefore, first, using a method based on constructing a priori estimates, we will determine the constraints on the parameters of the problem, under which it is globally solvable. The first, fundamental estimate, gives the initial information, starting from which one can receive step by step, moving up the scale of Banach spaces. To do this, the problem is reduced to a fixed-boundary problem through a change of variables. The resulting problem has timeand space-dependent coefficients with nonlinear terms. Next, Schauder-type a priori estimates are constructed for the equation with nonlinear terms and a fixed boundary. Based on these estimates, the uniqueness of the solution to the problem is proven. Then, the global existence of a solution to the problem was proved using the Leray-Schauder fixed point theorem