Results 121 to 130 of about 3,258,064 (367)

Singular integral equations with Cauchy kernels [PDF]

, 1946
W. J. Trjitzinsky
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A review of multiscale numerical modeling of rock mechanics and rock engineering

Deep Underground Science and Engineering, EarlyView.
Multiscale numerical methods of rock mechanics and rock engineering are reviewed, and the review results show that more attention should be paid to the development of an advanced constitutive model in addition to numerical techniques themselves. Abstract Rock is geometrically and mechanically multiscale in nature, and the traditional phenomenological ...
Xindong Wei, Zhe Li, Gaofeng Zhao
wiley   +1 more source

The general solution of the non-homogeneous Euler–Cauchy operator-differential equation with Neumann boundary conditions using the Laplace transform

Partial Differential Equations in Applied Mathematics
Many researchers are interested in topics related to solutions of differential equations with variable coefficients. Here for the first time, we study the nonhomogeneous second-order Euler–Cauchy operator-differential equation.
Abdel Baset I. Ahmed, Mohamed A. Labeeb
doaj  

The Cauchy Problem for Laplace's Equation in Three Dimensions [PDF]

, 1935
L. H. Johnson
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Damage modeling of CO2 injection well interfaces under coupled thermal, hydraulic and mechanical behavior

Deep Underground Science and Engineering, EarlyView.
This paper presents an investigation of CO2 injection well damage evolution considering different injection temperatures and the presence of a pre‐existing defect. The main outcome is that the accurate prediction of well leakage risk requires characteristics such as initial defects to be understood and represented in any modeling efforts. Abstract This
Lee J. Hosking, Xiangming Zhou
wiley   +1 more source

Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $|x|oinfty$

Electronic Journal of Differential Equations, 2012
We prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u) +h(t,u)$ with nonnegative bounded initial data.
Tatiana Kavitova
doaj  

Remarks on hyperstability of the Cauchy functional equation

, 2013
We present some simple observations on hyperstability for the Cauchy equation on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense), must be actually solutions
J. Brzdȩk
semanticscholar   +1 more source

Study on fracture parameter calibration and failure characteristics of rock with hole and crack

Deep Underground Science and Engineering, EarlyView.
The SIF and plastic zone equations for a single hole and crack have been derived. The model's failure state leads to the identification of four types of cracks. The plastic zone increases with increased brittleness and decreased crack length. Abstract Cracks within the surrounding rock of roadways significantly affect their stability and failure ...
Shaochi Peng, Wensong Wang
wiley   +1 more source

Partial difference equations arising from the Cauchy-Riemann equations

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2006
We consider some functional equations arising from the Cauchy-Riemann equations, and certain related functional equations. First we propose a new functional equation (E.1) below, over a $2$-divisible Abelian group, which is a discrete version of the ...
S. Haruki, S. Nakagiri
doaj  

On the Cauchy problem for equations with multiple characteristic roots [PDF]

, 1969
Tadayoshi Kano
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