diffusion equation


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diffusion equation

[də′fyü·zhən i′kwā·zhən]
(physics)
An equation for diffusion which states that the rate of change of the density of the diffusing substance, at a fixed point in space, equals the sum of the diffusion coefficient times the Laplacian of the density, the amount of the quantity generated per unit volume per unit time, and the negative of the quantity absorbed per unit volume per unit time.
More generally, any equation which states that the rate of change of some quantity, at a fixed point in space, equals a positive constant times the Laplacian of that quantity.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In this paper we consider IP1 for a more general diffusion equation that includes the operator (1.1) instead of the fractional derivative.
The multi-group diffusion equation comprises of the groups of neutrons of different energies diffusing within a nuclear reactor.
These include Lagergren first-order equation and pseudo- second-order equation, Elovich equation, Bangham's equation and intra-particle diffusion equation. The Lagergren first-order rate equation [14] is shown as follows:
Several well-established techniques have been proposed to enhance stability and accuracy of the optimal control problems governed by the steady convection diffusion equation, e.g., the streamline upwind/Petrov Galerkin (SUPG) finite element method [11], the local projection stabilization [5], the edge stabilization [27, 51], and discontinuous Galerkin methods [32, 52, 53, 54, 55].
By taking [V.sub.z] = 0, L = 1, W = 1, H = 1, this simply reduces to two-dimension advection three-dimension diffusion equation for transport of pollutants in street tunnel problem as discussed in [5]
In these systems, different species may diffuse and react [18-21], which implies considering suitable changes in the diffusion equation or in the boundary conditions to account for the processes of interest [18, 19, 22, 23].
Tan, "A third-order semi-implicit finite difference method for solving the one-dimensional convection diffusion equation," Applied Mathematical Modeling, vol.
This work examines the performance of a hybrid Laplace transform-Chebyshev collocation technique applied to the time-fractional diffusion equation in two dimensions with a nonlinear source term:
As a further step, Hegyi and Jung proved the generalized Hyers-Ulam stability of the diffusion equation on the restricted domain or with an initial condition (see [15,16]).
[19] proposed an LB model for fluid diffusion-convection with a chemical kinetic reaction using the double distribution function for controlling the fluid flow and diffusion, which introduced a source/sink term in the diffusion equation to govern the reaction process.
By combining these equations, the diffusion equation, that is, Fick's second law, results:

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