scholarly journals An $$L^2$$ approach to viscous flow in the half space with free elastic surface

2021 ◽  
Author(s):  
Reinhard Farwig ◽  
Andreas Schmidt
Keyword(s):  
Half Space ◽  
Lower Boundary ◽  
Strong Solutions ◽  
Plate Equation ◽  
Damping Term ◽  
Time Intervals ◽  
Elastic Surface ◽  
Inhomogeneous Boundary Data ◽  
Nonlinear Free Surface ◽  
Interaction Problem

AbstractWe consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in the half space $${\mathbb {R}}^n_+$$ R + n such that on the lower boundary a function h satisfying an undamped Kirchhoff-type plate equation is coupled to the flow field. Originally, h describes the height of an underlying nonlinear free surface problem. Since the plate equation contains no damping term, this article uses $$L^2$$ L 2 -theory yielding the existence of strong solutions on finite time intervals in the framework of homogeneous Bessel potential spaces. The proof is based on $$L^2$$ L 2 -Fourier analysis and also deals with inhomogeneous boundary data of the velocity field on the “free boundary” $$x_n=0$$ x n = 0 .

Influence of corrugated boundary surface and reinforcement of fibre-reinforced layer on propagation of torsional surface wave

2016 ◽  
Vol 23 (9) ◽  
pp. 1417-1436 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Anirban Lakshman ◽  
Amares Chattopadhyay
Keyword(s):  
Surface Wave ◽  
Dispersion Equation ◽  
Half Space ◽  
Boundary Surface ◽  
Lower Boundary ◽  
Transversely Isotropic ◽  
Wave Number ◽  
Torsional Surface Wave ◽  
Propagation Of Waves ◽  
Boundary Surfaces

These days fibre-reinforced materials are frequently used in construction sector for example in dams, bridges etc. Also the earth structure and artificial structure made by human may contain irregularity or corrugation, therefore, propagation of waves and vibrations through these structures gets affected by them. Motivated by these facts the present problem aims to study the propagation of torsional surface wave in a fibre-reinforced layer with corrugated boundary surface overlying an initially stressed transversely isotropic half-space. The closed form of the dispersion equation has been deduced and the notable effect of reinforcement, undulatory parameter of corrugated boundary surfaces of the layer, corrugation parameter of upper and lower boundary surfaces of the layer, initial stress acting in half-space and wave number on the phase velocity of torsional surface wave has been exhibited. The numerical computation along with graphical illustration has been carried out for fibre-reinforced layer of carbon fibre-epoxy resin and T300/5208 graphite/epoxy material for the transversely isotropic half-space. As a special case of the problem, deduced dispersion equation is found in well-agreement with the classical Love wave equation. Comparative study for reinforced and reinforced free layer has been performed and also depicted graphically. Moreover some analysis is made to highlight the important peculiarities of the problem.

On: “Magnetic anomalies of two‐dimensional bodies in a magnetic half‐space” by E. E. S. Sampaio (GEOPHYSICS, v. 47, p. 1229–1234, August, 1982).

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1800-1800
Author(s):  
L. Eskola
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Analytic Solution ◽  
Lower Boundary ◽  
Magnetic Anomalies ◽  
Additional Source ◽  
Field Problem ◽  
Susceptibility Contrast ◽  
The Magnetic Field ◽  
Upper Boundary

In a recent paper Sampaio presented an analytic solution of the magnetic field problem for a circular magnetized cylinder embedded in a homogeneous magnetized half‐space. In his paper, Sampaio also stated that the numerical method for solving magnetostatic problems by Eskola and Tervo (1980) doesn’t take into consideration the susceptibility contrast between the half‐space and the air. The model treated by Sampaio doesn’t actually exist, however. For a magnetized environment, in addition to the upper boundary, there is also a lower boundary, i.e., where the rock loses its magnetization (at least at the Curie point). This boundary holds an additional source of magnetic field that is of the same order of strength as the field caused by the upper boundary, if the horizontal dimensions of the magnetized environment are large. If the horizontal dimensions are not large, the effect of the vertical boundaries of the environment must also be taken into consideration. Eskola and Tervo (1980) find no difficulty in taking into consideration all the boundaries by means of their method.

Laser-Induced Heating of a Multilayered Medium Resting on a Half-Space: Part I—Stationary Source

1988 ◽  
Vol 55 (1) ◽  
pp. 93-97 ◽  
Author(s):  
R. Kant
Keyword(s):  
Laplace Transform ◽  
Half Space ◽  
Hankel Transform ◽  
Optical Recording ◽  
Time Intervals ◽  
Homogeneous Half Space ◽  
Multilayered Medium ◽  
Rule Application ◽  
The Laplace Transform ◽  
The Time Domain

Laser induced heating of a multilayered medium resting on a homogeneous half-space is considered. The transient heat transfer equation is solved by employing the Laplace transform in the time domain and the Hankel transform in the space domain (r direction). Numerical inversion of the Laplace transform is obtained by using a technique developed by Crump. For the time intervals of interest, inversion of the Hankel transform is obtained by the Simpson rule. Application to magneto-optical recording is discussed.

scholarly journals Study of a singular equation set in the half-space

2012 ◽  
Vol 142 (5) ◽  
pp. 897-915
Author(s):  
C. Amrouche ◽  
F. Dahoumane ◽  
G. Vallet
Keyword(s):  
Diffusion Coefficient ◽  
Half Space ◽  
Existence And Uniqueness ◽  
Formal Solution ◽  
Strong Solutions ◽  
Singular Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Image Position ◽  
Weak And Strong Solutions

This work is dedicated to the resolution of a singular equation set in the half-space, with a diffusion coefficient that blows up on the boundary. More precisely, for a datum g: ℝ+3 → ℝ, our problem involves seeking u: ℝ+3 → ℝ as a formal solution toWe give existence and uniqueness results of weak and strong solutions in suitable weighted spaces, where the weight depends on x3.

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