Guy Landsman, Shlomo Yanetz (Shlomo Chachanashvili

Existence and Uniqueness of a Solution for Nonlinear ODE and PDE Systems with Delay. An Application

abstract:
In this paper, we study the existence and uniqueness of a solution for a system of nonlinear differential equations with delay. We show its application using a mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. We also study a mathematical model that uses a system of nonlinear partial differential equations with delay while considering the geometrical configuration of the human bladder. We use two-dimensional grid discretization to find the numerical solution of the systems describing the tumor-immune interaction.

Mathematics Subject Classification: 34K99, 65M22, 92-10

Key words and phrases: Functional-differential equations, numerical methods for partial differential equations, mathematical modeling