Search results for "Boundary"
showing 10 items of 1626 documents
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
2018
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\ \partial\Omega \end{array}\right. \end{equation*} in a smooth bounded domain $\Omega$ of $\mathbb R^2$. The factor $\rho_{\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\varepsilon^{-1}$ in an $\varepsilon$-neighborhood of the boundary and to a constant of order $\varepsilon$ in the rest of $\Omega$. We study the asymptotic behavior of the eigenvalues $\lambda(\varepsilon)$ and the eige…
A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
2016
We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…
Parametric and nonparametric A-Laplace problems: Existence of solutions and asymptotic analysis
2021
We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain Ω. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to 0 + . In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators.
Multiplicity results for asymptotically linear equations, using the rotation number approach
2007
By using a topological approach and the relation between rotation numbers and weighted eigenvalues, we give some multiplicity results for the boundary value problem u′′ + f(t, u) = 0, u(0) = u(T) = 0, under suitable assumptions on f(t, x)/x at zero and infinity. Solutions are characterized by their nodal properties.
Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance
2007
Abstract Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.
Interaction of radiation fog with tall vegetation
1999
Abstract A one-dimensional radiation fog model is presented. It is coupled with a second model to include the effects of tall vegetation. The fog model describes in detail the dynamics, thermodynamics, and microphysical structure of a fog, as well as the interactions with the atmospheric radiative transfer. A two-dimensional joint size distribution for the aerosol particles and activated fog droplets is used, the activation of aerosol particles is explicitly modeled. The implications of the presence of tall vegetation on the state of the atmosphere and on the evolution of radiation fog are stated. It is shown that the existence of tall vegetation impedes the evolution of radiation fog. The …
A one-dimensional simulation of the interaction between land surface processes and the atmosphere
1992
A one-dimensional soil-vegetation model is developed for future incorporation into a mesoscale model. The interaction of land surface processes with the overlying atmosphere is treated in terms of three coupled balance equations describing the energy and moisture transfer at the ground and the energy state of the vegetation layer. For a complete description of the interaction, the coupled processes of heat and moisture transport within the soil are included as a multilayer soil model. As model verification, successful reproductions of the observed energy fluxes over vegetated surfaces from the HAPEX-MOBILHY experiment in southwestern France and from the LOTREX-10E/HIBE88 field experiment in…
What Flow Conditions are Conducive to Banner Cloud Formation?
2016
Abstract Banner clouds are clouds that are attached to the leeward slope of a steep mountain. Their formation is essentially due to strong Lagrangian uplift of air in the lee of the mountain. However, little is known about the flow regime in which banner clouds can be expected to occur. The present study addresses this question through numerical simulations of flow past idealized orography. Systematic sets of simulations are carried out exploring the parameter space spanned by two dimensionless numbers, which represent the aspect ratio of the mountain and the stratification of the flow. The simulations include both two-dimensional flow past two-dimensional orography and three-dimensional fl…
Multiyear in-situ measurements of atmospheric aerosol absorption properties at an urban coastal site in western Mediterranean
2016
Abstract In-situ aerosol absorption properties measured in Valencia (Spain) for four years, from February 2011 to February 2015, have been analysed. Spectral absorption properties have been obtained using a seven-wavelength Aethalometer AE-31 which covers the range from UV (370 nm) to IR (950 nm). In order to obtain the absorption coefficients, compensation parameters have been calculated for the Aethalometer considering seasonal and spectral differences. For this multiyear measurement period, seasonal site-specific calibration parameters have been obtained. Furthermore, estimations of the absorption Angstrom Exponent (α abs ) have been calculated using the seven Aethalometer wavelengths. T…
Evidence of ice crystals at cloud top of Arctic boundary-layer mixed-phase clouds derived from airborne remote sensing
2009
Abstract. The vertical distribution of ice crystals in Arctic boundary-layer mixed-phase (ABM) clouds was investigated by airborne remote-sensing and in situ measurements during the Arctic Study of Tropospheric Aerosol, Clouds and Radiation (ASTAR) campaign in March and April 2007. Information on the spectral absorption of solar radiation by ice and liquid water cloud particles is derived from airborne measurements of solar spectral radiation reflected by these clouds. It is shown by calculation of the vertical weighting function of the measurements that the observed absorption of solar radiation is dominated by the upper cloud layers (50% within 200 m from cloud top). This vertical weighti…