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On the Positivity Preserving Property of Hinged Plates
In this work we show that the Kirchhoff–Love model for a hinged plate $\Delta^2 v = f \text{ in }E,\; v = \Delta v - (1 - \sigma) \kappa v_n = 0\text{ on }\partial E$ admits, for $f \in L^2(E)$, a unique weak solution in W^{1,2}_0(E). Expand
On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions
We study the following nonlocal mixed order Gross-Pitaevskii equation $$i\,\partial_t \psi=-\frac{1}{2}\,\DeltaExpand
Comparison and sign preserving properties of bilaplace boundary value problems in domains with corners
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
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. ItExpand
Hinged and supported plates with corners
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 downwardlyExpand
Corners Give Problems When Decoupling Fourth Order Equations Into Second Order Systems
We compare both settings for the plate equation and prove that for planar domains with corners the system approach may fail to produce the correct solution. Expand
On the Hamiltonian structure of the planar steady water-wave problem with vorticity
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 presentedExpand
Comparing hinged and supported rectangular plates
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
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
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 modelExpand