Mathematical Sciences: Mathematical Models of Solid and Partially Solid Tumor Growth by Diffusion

这个项目的总体目标是开发和分析实体肿瘤扩散生长的数学模型。这些模型将描述肿瘤从最初的多细胞球体演变而来，考虑到营养物质和生长抑制因子在肿瘤内的扩散。该项目涉及的数学包括研究非线性扩散方程和积分-微分方程组。这些方程的解的存在性、唯一性、稳定性和定性行为的问题将被讨论。

The general objective of this project is the development and analysis of mathematical models of solid tumor growth by diffusion. The models will describe the evolution from an initial multicellular spheroid of a tumor, taking into account the diffusion of nutrient and growth-inhibitory factors within the tumor. The mathematics involved in the project includes the study of nonlinear diffusion equations and integro-differential equations. Questions of existence, unicity, stability, and qualitative behavior of solutions to these equations will be addressed.