Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 16 of 16 for “"Nonlinear PDE"”.
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Nonlinear PDE and Optical Surfaces Design
We introduce two models to design near field reflectors in R^3 that solve an inverse problem in radiometry, taking into account the inverse square law of irradiance. The problem leads to a Monge-Ampere type inequality. The surfaces in the first model are strictly convex and require to be far from …
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Sparse Learning of Nonlinear PDE Dynamics using Kalman Smoothing
… or explicitly. The Sparse Identification of Nonlinear Dynamics (SINDy) method achieves this in two steps: a derivative estimation and smoothing step, followed by sparse regression over a library of candidate functions. Previous implementations of the derivative step in SINDy, including the …
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Anisotropic nonlinear PDE models and dynamical systems in biology
… analysis and numerical simulation of anisotropic nonlinear partial differential equations (PDEs) and dynamical systems in biology. It is divided into two parts, motivated by the simulation of fingerprint patterns and the modelling of biological transport networks. The first part of this thesis …
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An approximation to the solution of hyperbolic equation by homotopy analysis method
… of the class of Partial Differential Equation (PDE). PDE is one of the basic areas of applied analysis, and it is difficult to imagine any area of applications where its impact is not felt. In recent decades, there has been tremendous emphasis on understanding and modelling nonlinear processes …
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Local Regularity of the Complex Monge-Ampere Equation
… Monge-Ampere equation through the modern fully-nonlinear PDE point of view. We have apply the modern elliptic techniques to establish new local regularity results. These includes: regularity of small perturbed solutions, Holder regularity of the Hessian of the W^{2,p} solutions and a …
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A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
… and the Fokker- Planck equation. Certain PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on triangle mesh surfaces. To address this challenge, we leverage a splitting integrator combined with a convex optimization step to solve these PDE. …
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Infinitely Many Solutions to Asymmetric, Polyharmonic Dirichlet Problems
… on the existence of infinitely many solutions to nonlinear partial differential equations that are perturbed from symmetry. Our main theorems focus on polyharmonic Dirichlet problems with exponential nonlinearities, and are now published in Topol. Methods Nonlinear Anal. Vol. 50, No.1, (2017), …
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Numerical Solution Techniques for Reaction Parameter Sensitivity Coefficients in Multicomponent Subsurface Transport Models
… transport, the state equations consist of a nonlinear PDE for each aqueous component and a nonlinear ODE for each immobile component; these differential equations are coupled together through reaction source/sink terms. The corresponding sensitivity equations take the form of a system of …
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On Generalized Solutions to Some Problems in Electromagnetism and Geometric Optics
… Optimal Transport techniques; as such, a fully nonlinear PDE of Monge-Amp\`ere type arises here.
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On gravity-driven flow
… in an annular geometry we derive the governing nonlinear PDE for the evolution of the density interface. Systematically varying the initial conditions leads to the recognition that there are different routes to equilibrium. Asymptotic analysis of squeezing and draining limits allows us to find …
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Analysis of Instabilities in Microelectromechanical Systems, and of Local Water Slamming
… semi-infinite perfect conductor. The coupled nonlinear partial differential equations (PDEs) for mechanical deformations are solved numerically by the finite element method (FEM) and those for the electrical problem by the boundary element method. The coupled nonlinear PDE governing transient …
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Distributed parameter control of heat diffusion with solidification
… the temperature of the steel is governed by a nonlinear partial differential equation (PDE), which presents a challenge for existing control techniques. In the first part of this dissertation, the state-of-the art in industrial control systems for this process is described. The primary …
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Control of constrained moving-boundary process with application to steel continuous casting
… feedback control techniques for coping with the nonlinear moving boundary problem dynamics. The present work provides several key building blocks towards a comprehensive solution of the continuous steel casting feedback control problem. In the first part of this dissertation, a mathematical model …
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Collective behaviour of active particles with mean-field interaction
… a macroscopic partial differential equation (PDE) from a nonlinear interacting stochastic particle system used to model ants and use the PDE to provide a phase diagram for the collective behaviour of the particle model. The PDE model sustains ants forming bidirectional lanes and ants forming …
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Computational modelling of global haemodynamics and its interaction with cerebrospinal fluid and brain dynamics with application to essential hypertension
… mathematical model. It includes one-dimensional, nonlinear PDE systems for major blood vessels and zero-dimensional, differential-algebraic systems for the remaining components. Highlights include the viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous; …
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Modeling Temperature Dependence in Marangoni-driven Thin Films
<p>Thin liquid films are often studied by reducing the Navier-Stokes equations</p><p>using Reynolds lubrication theory, which leverages a small aspect ratio</p><p>to yield simplified governing equations. In this dissertation a plate</p><p>coating application, in which polydimethylsiloxane coats a …