Browsing by Subject "Partial"
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Item Construction of a fundamental solution for a class of time degenerate parabolic equations(Texas Tech University, 1972-05) Drummond, John CNot availableItem Control of distributed parameter systems(Texas Tech University, 1986-12) Tubach-Ley, Wilhelmina BarbaraNot availableItem Estimates on solutions of second order partial differential equations(Texas Tech University, 1974-05) Walker, Billy KennethNOT AVAILABLEItem Exact solutions in non-linear diffusion(Texas Tech University, 1995-05) South, Michael J.The nonlinear diffusion equation, {w{u)ux)x — Ut, has application in many areas of science and technology. We discuss exact solutions of this equation for three weight functions-w"^, e", and \n{u). We obtain these solutions in each case by "inverting the weight function," that is, we make the substitution v = w{u) and solve the resulting equation for v. Although we do not use similarity techniques, most of our solutions turn out to be similarity solutions-a brief look at similarity methods is presented. The solution we find for ln{u) appears not to have been published.Item Superconvergence of convection-diffusion equations in two dimensions(Texas Tech University, 1999-12) Moran, Daniel L.This thesis studies the convergence of a singularly perturbed two-dimensional problem of the convection-diflfusion type. The problem is solved using the bilinear finite element method on a Shishkin Mesh. This thesis will consider the results of two separate types of Shishkin Meshes, as well as a quick consideration of the uniform mesh and its shortcomings. Results will show a superconvergence rate close to 0 using a discrete energy norm. Results will also consider stability of the method by examining the condition number of the element stiffness matrix.Item System identification and model-based control for a class of distributed parameter systems(Texas Tech University, 2003-05) Zheng, DaguangA large number of processes in the chemical and petroleum industries are distributed in nature. The diversity of distribution patterns and functions make modeling of distributed parameter systems (DPS) a very challenging problem. Employment of first principles about the physics and chemistry will yield mathematical models in the form of systems of linear or nonlinear partial differential equations (PDEs). The analytical and numerical solutions for PDEs are infinite or very high dimension, which are not suitable for implementable control designs. The first objective of this research is to develop a general model reduction methodology to reduce the system of PDEs to a finite dimensional system of ODEs, which can be used to synthesize a model-based control. This methodology is based on the identification of empirical eigenfunctions (EEFs) from data and using the Galerkin method to obtain a model with dominant modes. For a system of first-order hyperbolic PDEs, accelerated EEFs are used to find a reduced-order model. In the case where the physics-based modeling approach cannot be applied with confidence, an input/output model developed based on experimental data may suffice. A novel system identification method to develop the model using a data-driven approach is proposed. The method combines the fundamental principles of singular value decomposition (SVD) and Karhunen-Loeve (KL) expansion in the identification of a finite order model. The application of SVD and KL provides natural decoupling of the inputs and outputs while yielding a model that captures the dominant spatial and temporal behavior of the distributed system. The fundamental theorems to assure the accuracy of this method are provided. Implementable control designs to regulate the DPS are now realizable with a finite order model. Dynamic matrix control (DMC) and Quadratic DMC (QDMC) are selected as control strategies, wherein the merit of the control design is dependent on the fidelity of the identified by SVD-KL method. Sufficient conditions are proposed to tune the QDMC control strategy so that stable closed-loop performance is guaranteed. The regulation of several candidate chemical reactor systems and the hydro-dealkylation process that produces benzene from toluene (HDA) are used to illustrate the potential of this data-driven modeling and model-based control framework for distributed parameter systems.Item Time degenerate parabolic equations(Texas Tech University, 1971-05) Waid, Margaret CowsarNot available