Existence and uniqueness of a solution for nonlinear ODE and PDE systems with delay. An application. (English) Zbl 1504.34153

Landsman, Guy; Yanetz, Shlomo (Shlomo Chachanashvili)

Mem. Differ. Equ. Math. Phys. 86, 113-126 (2022).

Summary: 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.

MSC:

34K05	General theory of functional-differential equations
35R10	Partial functional-differential equations
34K17	Transformation and reduction of functional-differential equations and systems, normal forms
65M22	Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
92C37	Cell biology
34C60	Qualitative investigation and simulation of ordinary differential equation models
34K60	Qualitative investigation and simulation of models involving functional-differential equations

Keywords:

functional-differential equations; numerical methods for partial differential equations; mathematical modeling