Global ETD Search
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Showing 1 to 15 of 15 for “"viscosity solutions"”.
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Qualitative Properties Of Solutions Of Fully Nonlinear Equations And Overdetermined Problems
… the maximum principles and radial symmetry for viscosity solutions of fully nonlinear partial differential equations. We</p> <p>obtain the radial symmetry and monotonicity properties for</p> <p>nonnegative viscosity solutions of fully nonlinear equations under some asymptotic decay rate at …
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Contraction/expansion flow of dilute elastic solutions in microchannels
… of extensional flows of mobile dilute polymer solutions in microchannel. By observing such fluids on the microscale it is possible to generate large strain rates ([approximately] 50,000 s⁻¹) that are greater than values which have been observed in macroscale contraction flows. Subsequently, …
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Regularity of the Level Set Equation for Mean Curvature Flow with an Axis of Symmetry
In this thesis we study the regularity of viscosity solutions to the level set equation for mean curvature flow. We describe a set of hypotheses under which we can prove that the level sets of these solutions are C¹,¹ submanifolds of spacetime with well understood behavior near singular times. We …
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Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients
<p>In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity …
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A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
… reaction-diffusion systems. Using the theory of viscosity solutions, I give a proof which extends the previous theorem to no longer require any regularity assumptions on the boundary of the convex set in which the system takes its values. The second result is an approximation scheme for reflected …
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The Reflected Quasipotential: Characterization and Exploration
… The characterization will need to be in terms of viscosity solutions. Solutions are not unique, thus additional qualifications will be needed for uniqueness. In order to prove our uniqueness result we consider a discounted version of V(x) in a truncated region and pass to the limit. In addition to …
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Optimal control of quantum systems using dynamic programming
… interpretation of this cost function in terms of viscosity solutions of the associated Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) over the manifolds of interest. This framework is applied to explore optimal control strategies for drift and drift-less quantum systems that …
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Optimal control of quantum systems using dynamic programming
… interpretation of this cost function in terms of viscosity solutions of the associated Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) over the manifolds of interest. This framework is applied to explore optimal control strategies for drift and drift-less quantum systems that …
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Electromechanics and electrorheology of fluid flow with internal micro-particle electrorotation
… general governing equations in the zero spin viscosity and the finite spin viscosity small spin velocity limits for both Couette and Poiseuille flow geometries. In the zero spin viscosity limit, expressions for the spin velocity and effective viscosity of Couette flow as well as the spin …
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Agitation, mixing and mass transfer in simulated high viscosity fermentation broths
… m\(^3\), unaerated liquid height = 0.3 m. The solutions of sodium carboxymethylcellulose used exhibit moderate viscoelasticity and shear thinning behaviour, obeying the power law over the range of shear rates studied. The gas-liquid mass transfer was studied using a steady state technique. This …
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Robust Control for Hybrid, Nonlinear Systems
… for the associated dissipative system) with solutions of the appropriate variational inequality (VI). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense. It also happens that a positive definite supersolution of the VI can be used for stability …
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Understanding self-assembly and flow heterogeneities in poloxamer wormlike micelles
… ionic surfactants, WLMs can also form in solutions of amphiphilic block polymers. The most well-studied of these are poloxamers, ABA block polymers formed from two polyethylene oxide (PEO) end blocks and one polypropylene oxide (PPO) midblock. Poloxamers have the potential to form WLMs …
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New and old sub-Riemannian challenges bridging analysis and geometry
The aim of this thesis is to propose a systematic exposition of some analytic and geometric problems arising from the study of sub-Riemannian geometry, Carnot-Carathéodory spaces and, more broadly, anisotropic metric and differential structures. We deal with four main topics. 1 Calculus of …
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Literature review of the use of common protective coatings for concrete structures with experiences in the South African context
… follows: HYDROPHOBIC IMPREGNATION These are low viscosity fluids which penetrate several millimetres into the concrete and considerably increase the water penetration resistance of concrete, whilst still allowing the passage of water vapour and gases. Typical examples are silanes and siloxanes. …