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fotouhi-firoozabad--morteza
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A Multiscale Moving Boundary Model For Cancer Invasion
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firoozabad, Morteza (Supervisor)
Abstract
Cancer invasion of tissue is a key aspect of the growth and spread of cancer and is crucial in the process of metastatic spread i.e. the growth of secondary cancers. Invasion consists in cancer cells secreting various matrix degrading enzymes (MDEs) which destroy the surronding tissue or extracellular matrix (ECM). Through a combination of proliferation and migration, the cancer cells then actively spread locally into the surrounding tissue. Thus processes occuring at the level of individual cells eventually give rise to processes occuring at the tissue level. In this thesis we introduce a new type of multiscale model describing the process of cancer invasion of tissue.Our multiscale model...
Singular PDEs with Irregular Data
, Ph.D. Dissertation Sharif University of Technology ; Hesaaraki, Mahmoud (Supervisor) ; Fotouhi Firoozabad, Morteza (Co-Supervisor)
Abstract
Singular differential equations have a wide range of applications. Hardy singularities, which are connected to inequalities of the same name and have various extensions, are the most well-known singularities. The application of Hardy inequalities in quantum physics and also in the linearization of reaction-diffusion equations in thermodynamics and combustion theory motivates researchers to examine them. Singularities on a domain's boundary are another well-known type of singularity. In the study of fluid mechanics and pseudoplastic flows, these singularities emerge.Differential equations with coefficients or functions that are simply functions belonging to $ L^1 $, or bounded Radon measures,...