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Full-Text Articles in Physical Sciences and Mathematics
Energy Methods For Reaction-Diffusion Problems, Xing Zhong
Energy Methods For Reaction-Diffusion Problems, Xing Zhong
Dissertations
Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally studied in the context of combustion modeling.
For suitable nonlinearity and a monotone increasing one-parameter family of initial data starting with zero data, small values of the parameter lead to extinction, whereas large values of the parameter may lead to spreading, i.e., the solution converging locally uniformly to a positive spatially independent …
Mathematical Models Of Combustion At High Pressure, Daniel Fong
Mathematical Models Of Combustion At High Pressure, Daniel Fong
Dissertations
In this dissertation, we develop new mathematical theories of flame propagation that are valid at elevated, or extreme, pressures. Of particular interest is the regime of burning in which the pressure exceeds the critical pressure of the species undergoing chemical reaction. Fluids and flames are known to behave differently under these extreme conditions as opposed to atmospheric pressure. The focus of this dissertation is to investigate these differences by deriving reduced models that contain the unique features.
In the first part of this dissertation, we analyze the structure of laminar diffusion flames at high pressure in the limit of large …