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of 72
pro vyhledávání: '"Pelloni, Beatrice"'
We study the presence of a non-trivial revival effect in the solution of linear dispersive boundary value problems for two benchmark models which arise in applications: the Airy equation and the dislocated Laplacian Schr{\"o}dinger equation. In both
Externí odkaz:
http://arxiv.org/abs/2403.01117
Autor:
Pelloni, Beatrice, Smith, David A.
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the spatial opera
Externí odkaz:
http://arxiv.org/abs/2402.03133
The mysterious phenomena of revivals in linear dispersive periodic equations was discovered first experimentally in optics in the 19th century, then rediscovered several times by theoretical and experimental investigations. While the term has been us
Externí odkaz:
http://arxiv.org/abs/2308.09961
Autor:
Egan, Charlie P., Bourne, David P., Cotter, Colin J., Cullen, Mike J. P., Pelloni, Beatrice, Roper, Steven M., Wilkinson, Mark
Publikováno v:
Journal of Computational Physics, Volume 469, 111542 (2022)
We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The geometric method is a Lagrangian discretisation,
Externí odkaz:
http://arxiv.org/abs/2203.04903
Publikováno v:
Proceedings of the Royal Society A (2021) 477:20210241
We study the phenomenon of revivals for the linear Schr\"odinger and Airy equations over a finite interval, by considering several types of non-periodic boundary conditions. In contrast with the case of the linear Schr\"odinger equation examined rece
Externí odkaz:
http://arxiv.org/abs/2103.01663
We present and analyse a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations, in the concrete case of three nonlocal equations that arise in water wave theory and are defined by convolution kernels. Revival
Externí odkaz:
http://arxiv.org/abs/2010.01320
Publikováno v:
Calculus of Variations and Partial Differential Equations, Volume 61, Article number: 39 (2022)
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof
Externí odkaz:
http://arxiv.org/abs/2009.04430
We study initial boundary value problems for linear evolution partial differential equations (PDEs) posed on a time-dependent interval $l_1(t)
Externí odkaz:
http://arxiv.org/abs/1908.03729
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The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in a three-d
Externí odkaz:
http://arxiv.org/abs/1811.03926