Global ETD Search
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Showing 1 to 7 of 7 for “"non-linear PDE"”.
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Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation.
… of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish this task, the non-classical method is utilized to find the <em>infinitesimal generator</em> and the <em>invariant surface condition</em> for the subgroup where the …
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Pattern-forming in non-equilibrium quantum systems and geometrical models of matter
… condensates can be modelled by means of a non-linear PDE which is strictly related to the Gross-Pitaevskii and the complex Ginzburg-Landau equations. Numerical simulations of this equation are used to investigate the robustness of the rotating vortex lattice which is predicted to …
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Asymptotic Behaviour and Derivation of Mean Field Models
… 5 and 6 prove an instability criterion for non-monotone equilibria of the Vlasov-Maxwell system. In Chapter 5 we study a related problem in approximation of the spectra of families of unbounded self adjoint operators. In Chapter 6 we show how the instability problem for Vlasov-Maxwell can be …
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A methodology for non-Intrusive projection-based model reduction of expensive black-box PDE-based systems and application in the many-query context
… of the work is that it converts the original non-linear PDE system into a linear PDE system with auxiliary non-linear algebraic equations which are then projected onto the POD subspace. By such a linearization, it is shown that the governing equations can be extracted by directly discretizing …
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Dynamics and Statics of Liquid-Liquid and Gas-Liquid interfaces on Non-Uniform Substrates at the Micron and Sub-Micron Scales
… (small Capillary, Weber, and Bond numbers), non-equilibrium at the contact line of sessile bubbles and droplets can influence geometries and dynamics. First, the wetting of micron-sized ellipsoidal particles was considered. In the space of axially symmetric interfaces, it is found that …
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Statistical inference and computation in elliptic PDE models
Partial differential equations (PDE) are ubiquitous in describing real-world phenomena. In many statistical models, PDE are used to encode complex relationships between unknown quantities and the observed data. We investigate statistical and computational questions arising in such models, adopting …
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Conformal pseudo-metrics and some applications
… of basic open problems in conformal geometry and non-linear PDE. One of our results is a solution to Problem 1 for arbitrary simply connected domains. However, we shall see that our approach has also some other ramifications, for instance to a well-known problem due to Rellich and Wittich in PDE. …