Blow-up For Chemotaxis Models

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Sharifi Tabar, Mohsen | 2010

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 41109 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
Moving of living organisms appears in many interesting problems, e.g. the growth of bacteria colonies, tumor growth, wound healing, color patterns of animals and etc. There are many ways to model such problems and PDE theory is widely used to investigate these problems. In this thesis, we study two well-known classic models. First, macroscopic “Keller–Segel” model and then kinetic “Othmer–Dunbar–Alt” System. Since these models have a nice behavior in two dimensions that they don’t have in other dimensions, we propose a way to alter them such that they behave in this way in all dimensions. Also none of the known models have the suitable dynamics in one dimension, so our model has the property that it may be applied in dimension one and numerical simulations can be easily done to calculate the solutions. Also we have two chapters which are of independent interest and they are devoted to the properties of Sobolev
Keywords:
Hilbert Transform ; Numerical Simulation ; Blow-Up ; Chemotaxis ; Biology ; Discrete Fourier Transform