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  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 , the local projection stabilization , 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 
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.
Einstein's analysis was based on the diffusion equation
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]).
 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: