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On the Positivity Preserving Property of Hinged Plates

- E. Parini, A. Stylianou
- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 11 December 2009

TLDR

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

- Yongming Luo, A. Stylianou
- Mathematics
- 14 February 2019

We study the following nonlocal mixed order Gross-Pitaevskii equation $$i\,\partial_t \psi=-\frac{1}{2}\,\Delta… Expand

Comparison and sign preserving properties of bilaplace boundary value problems in domains with corners

- A. Stylianou
- Mathematics
- 2010

This work is focused on the study of the Kirchhoff-Love model for thin, transversally loaded plates with corner singularities on the boundary. The former consists in finding a real valued function u,… Expand

Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation

- M. Groves, David J. B. Lloyd, A. Stylianou
- Mathematics
- 25 October 2016

Abstract We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It… Expand

Hinged and supported plates with corners

- S. Nazarov, A. Stylianou, G. Sweers
- Physics
- 2 February 2012

We consider the Kirchhoff–Love model for the supported plate, that is, the fourth-order differential equation Δ2u = f with appropriate boundary conditions. Due to the expectation that a downwardly… Expand

Corners Give Problems When Decoupling Fourth Order Equations Into Second Order Systems

- T. Gerasimov, A. Stylianou, G. Sweers
- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 19 June 2012

TLDR

On the Hamiltonian structure of the planar steady water-wave problem with vorticity

- M. Groves, A. Stylianou
- Mathematics
- 1 March 2014

Abstract We consider the stream-function formulation of the hydrodynamic problem for steady rotational water waves both with and without surface tension. A natural Lagrangian formulation is presented… Expand

Comparing hinged and supported rectangular plates

- A. Stylianou, G. Sweers
- Mathematics
- 1 September 2010

Abstract We consider the Kirchhoff–Love model for the supported plate, that is, the fourth order differential equation Δ 2 u = f ⩽ 0 in a two-dimensional bounded domain Ω with the condition u | ∂ Ω ⩾… Expand

Global attractor for some wave equations of $p-$ and $p(x)-$Laplacian type

- N. Stavrakakis, A. Stylianou
- Mathematics
- 20 January 2011

We study the existence of solutions for the equation utt − ∆p(x)u − ∆ut + g(u) = f(x, t), x ∈ Ω (bounded) ⊂ IR, t > 0 in both the isotropic case (p(x) ≡ p, a constant) and the anisotropic case (p(x)… Expand

A dipolar Gross-Pitaevskii equation with quantum fluctuations: Self-bound states

- Yongming Luo, A. Stylianou
- Physics
- 2 June 2018

We prove existence and qualitative properties of standing wave solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation (GPE), the latter being currently the state-of-the-art model… Expand

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