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Numerical Solutions of Generalized Burgers' Equations for Some Incompressible Non-Newtonian FluidsShu, Yupeng 11 August 2015 (has links)
The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.
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[en] EXISTENCE, UNIQUINESS AND STABILITY OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS SYSTEMS / [pt] EXISTÊNCIA, UNICIDADE E ESTABILIDADE DE SOLUÇÕES DE SISTEMAS DE EQUAÇÕES DIFERENCIAIS ORDINÁRIASFERNANDO SILVA BRAGA 26 April 2021 (has links)
[pt] Esta dissertação tem o objetivo de aplicar os conceitos e ferramentas da
Análise Real e Álgebra Linear num estudo sobre a teoria de existência, unicidade
e estabilidade de soluções de sistemas de equações diferenciais ordinárias,
considerando sistemas gerais parametrizados, lineares e não-lineares. / [en] This dissertation aims to apply the concepts and tools of Real Analysis
and Linear Algebra to the theory of existence, uniquiness and stability of
solutions of ordinary differential equations systems, considering general parametric,
linear and non-linear systems.
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