The One-Dimensional Stationary Diffusion Equation

1983 ◽  
pp. 91-158
Author(s):  
G. I. Marchuk ◽  
V. V. Shaidurov
Keyword(s):  
Diffusion Equation ◽  
One Dimensional ◽  
Stationary Diffusion ◽  
Stationary Diffusion Equation ◽  
The One

Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

2018 ◽  
Vol 284 ◽  
pp. 1230-1234
Author(s):  
Mikhail V. Maisuradze ◽  
Alexandra A. Kuklina
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Differential Diffusion ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Diffusion ◽  
Simplified Algorithm ◽  
The One ◽  
Carburizing Process ◽  
Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

scholarly journals Unique continuation principle for the one-dimensional time-fractional diffusion equation

2019 ◽  
Vol 22 (3) ◽  
pp. 644-657 ◽  
Author(s):  
Zhiyuan Li ◽  
Masahiro Yamamoto
Keyword(s):  
Diffusion Equation ◽  
Anomalous Diffusion ◽  
Function Method ◽  
Unique Continuation ◽  
Fractional Diffusion ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
Continuation Principle ◽  
Time Fractional Diffusion Equation ◽  
The One

Abstract This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order α ∈ (0, 1). Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle.

Gravity-induced wrinkle lines in vertical membranes

1981 ◽  
Vol 375 (1762) ◽  
pp. 307-325 ◽  
Keyword(s):  
Heat Flow ◽  
Diffusion Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Prime Objective ◽  
Flow Through ◽  
Flexible Membranes ◽  
The One

A theory is presented for the behaviour under self-weight of inextensible but perfectly flexible membranes supported in a vertical plane. Slack in the membrane manifests itself in the formation of (curved) wrinkle lines whose determination is the prime objective. The equilibrium and strain conditions are derived and solutions are given for several simple cases. It is shown that the wrinkle lines satisfy the one-dimensional diffusion equation and hence there are analogies, for example, with heat flow through a slab.

On some projections of homogenised coefficients for stationary diffusion equation

PAMM ◽  
2003 ◽  
Vol 3 (1) ◽  
pp. 440-441 ◽  
Author(s):  
Nenad Antonić ◽  
Marko Vrdoljak
Keyword(s):  
Diffusion Equation ◽  
Stationary Diffusion ◽  
Stationary Diffusion Equation
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