Unique solvability of the boundary value problem modeling the distribution of partial pressure of oxygen in the Krogh cylinder
Abstract
A nonlinear model of oxygen transport in the Krogh cylinder is studied. The model is of the 3D – 1D type and includes a nonlinear diffusion equation which describes oxygen transport and its consumption in tissue, and a nonlinear ODE of convective oxygen transport in a blood vessel. Using appropriate conjugation conditions, the model also describes the penetration of oxygen into tissues through the capillary wall. In the current work, the nonlocal unique solvability of the boundary value problem is proved. A numerical algorithm is constructed, and its convergence is established. The numerical experiments illustrate the influence of low hematocrit and reduced blood flow rate on the hypoxia effect.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Mathematical Biology Tumor Growth
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 31
- Issue
- 0
- Pages
- 187–198
- Publication date
- 27 February 2026
- Language
- EN