Search results for "boundary"

Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2

2009

AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

Infinitely many solutions for a mixed boundary value problem

2010

The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.

Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

2019

In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.

Time-based Chern number in periodically driven systems in the adiabatic limit

2023

To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic two-dimensional (2D) Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic 2D Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via h…

Non-Local Scattering Kernel and the Hydrodynamic Limit

2007

In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.

Explicit closed form solutions of boundary value problems for systems of difference equations

1990

In this paper boundary value problems for systems of difference equations of the type , where A j ∈ C p×p and bn y j+n ∈ C p , for 0≤j≤k − 1, are studied from an algebraic point of view. Existence conditions and closed form solutions are given in terms of co-solutions of the algebraic matrix equation .

Simplified Model to Predict Runoff Generation Time for Well-Drained and Vegetated Soils

2016

The study of generation process of subsurface stormflow, typical of well-drained and high permeable soils, can be theoretically carried out by applying the continuity and the motion equations with the appropriate boundary conditions. However, difficulties and uncertainness on determining soil hydraulic properties and soil physics heterogeneities let this way not always feasible. In a different way, processes dynamic can be derived by the local scale through a coarse graining procedure, allowing to preserve medium motion character, while hydraulic fluctuation of the motion are lost. Following an approach as this, in this paper a simplified model to predict the runoff generation time, the so-…

Recovery of time-dependent coefficients from boundary data for hyperbolic equations

2019

We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.

Miami, tourists, colonists and adventurers in the last boundary of Latin America

2012

An orbital floating time scale of the Hauterivian/Barremian GSSP from a magnetic susceptibility signal (Río Argos, Spain).

2012

10 pages; International audience; An orbital floating time scale of the HauterivianeBarremian transition (Early Cretaceous) is proposed using high-resolution magnetic susceptibility measurements. Orbital tuning was performed on the Río Argos section (southeast Spain), the candidate for a Global boundary Stratotype Section and Point (GSSP) for the HauterivianeBarremian transition. Spectral analyses of MS variations, coupled with the frequency ratio method, allow the recognition of precession, obliquity and eccentricity frequency bands. Orbitallytuned magnetic susceptibility provides minimum durations for ammonite biozones. The durations of well-constrained ammonite zones are assessed at 0.78…