Localization of Solutions to Equations of Tumor Dynamics

Abstract

This article discusses a mathematical model of tumor dynamics. The tissue is considered as a multiphase three-component medium consisting of extracellular matrix, tumor cells, and extracellular fluid. The extracellular matrix is generally deformable. In the case of the predominant extracellular fluid — tumor cell interaction, the original system of equations is reduced to the one parabolic equation degenerating on the solution with a special right-hand side. The property of a finite perturbation propagation velocity for tumor cell saturation is revealed. The introduction describes the essence of the problem. The second part presents the derivation of a mathematical model of tumor dynamics as a three-phase medium. The third part describes a mathematical model for the case when mechanical interaction with extracellular fluid is neglected. The fourth part considers the case of predominant fluid-cell interaction. The fifth part provides a proof of the theorem on the localization of the solution to the equation for the saturation of tumor cell.

Keywords

• differential equations
• filtration
• tumor
• localization
• porosity