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

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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.