Uniqueness problem and growth property for Fourier transform of functions in the upper half-space

2020 ◽  
pp. 1-8
Author(s):  
Zuoliang Xu ◽  
Yanhui Zhang
Keyword(s):  
Fourier Transform ◽  
Half Space ◽  
Uniqueness Problem ◽  
Growth Property

Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

1978 ◽  
Vol 45 (4) ◽  
pp. 812-816 ◽  
Author(s):  
B. S. Berger ◽  
B. Alabi
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Half Space ◽  
Coordinate Transformation ◽  
Numerical Results ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

A Fast Method for Solving Contact Plasticity in a Half Space

2011 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Residual Stresses ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Three Dimensional ◽  
New Method ◽  
Fast Method ◽  
Discrete Convolution ◽  
Influence Coefficients ◽  
The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

Poisson’s integral formula via heat kernels

Analysis ◽  
2019 ◽  
Vol 39 (2) ◽  
pp. 59-64
Author(s):  
Yoichi Miyazaki
Keyword(s):  
Fourier Transform ◽  
Heat Kernel ◽  
Half Space ◽  
Unbounded Domain ◽  
Harmonic Functions ◽  
Integral Formula ◽  
Heat Kernels ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Fourier Transform

Abstract We give another proof of Poisson’s integral formula for harmonic functions in a ball or a half space by using heat kernels with Green’s formula. We wish to emphasize that this method works well even for a half space, which is an unbounded domain; the functions involved are integrable, since the heat kernel decays rapidly. This method needs no trick such as the subordination identity, which is indispensable when applying the Fourier transform method for a half space.

scholarly journals CLASSICAL SOLUTION OF THE CAUCHY PROBLEM FOR BIWAVE EQUATION: APPLICATION OF FOURIER TRANSFORM

2012 ◽  
Vol 17 (5) ◽  
pp. 630-641 ◽  
Author(s):  
Victor Korzyuk ◽  
Nguyen Van Vinh ◽  
Nguyen Tuan Minh
Keyword(s):  
Cauchy Problem ◽  
Exact Solution ◽  
Fourier Transform ◽  
Fourier Analysis ◽  
Classical Solution ◽  
Half Space ◽  
Analysis Techniques ◽  
The Cauchy Problem

In this paper, we use some Fourier analysis techniques to find an exact solution to the Cauchy problem for the n-dimensional biwave equation in the upper half-space ℝ n × [0, +∞).

Thermoelastic Solutions for Thermal Distributions Moving Over Half Space Surfaces and Application to the Moving Heat Source

1988 ◽  
Vol 55 (1) ◽  
pp. 87-92 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Fourier Transform ◽  
Heat Source ◽  
Half Space ◽  
Elastic Half Space ◽  
Temperature Wave ◽  
Exact Results ◽  
Moving Heat Source ◽  
Exponential Fourier Transform

A method is developed for obtaining fundamental thermal and thermoelastic solutions for thermal distributions moving over the surface of an elastic half space. This method uses the concept of a moving temperature wave along with a novel form of an exponential Fourier transform. The technique is developed and then demonstrated on the example of a moving heat source. Exact results are matched with results from Carslaw and Jaeger (1959) and Barber (1984).

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