The numerical solutions of the advection-diffusion equation are themselves numerous and sometimes very sophisticated, in order to avoid two undesirable features: oscillatory behavior and numerical diffusion. It is known that the common practice of “splitting-up” the solution is not always the best approach to the advection-diffusion problem. By using the ordinary differential equation analogy m...

Abstract. The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a composite medium with optically thin inclusions in an optically thick background medium. The equation governing the evolution of the approximat...

Image data restoration by diffusion equation is now a well established approach since the pioneering work of Perona and Malik (Perona & Malik, 1990). Originally, image diffusion consists in a convolution by a Gaussian kernel which introduces a scale dimension related to the standard deviation of the Gaussian kernel t 2 = σ . This convolution is equivalent to solve the following linear diffusion...

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J ∗u−u+G ∗ (f(u))− f(u) in R, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equatio...

the release of fe from soil solid phases into soil solution is a dynamic process that regulates the continuous supply of this element to growing plants. to ascertain the pattern of fe release, the kinetics of fe release from six soils by diethylenetriaminepentaacetic acid (dtpa) solution were investigated using soil samples taken from two different agroclimatic regions of iran. all soils were c...

Stochastic differential equations have a built-in direction of time flow since future increments in the driving process are assumed independent of present and past values of the process defined by the solution of the equation. The differential equations are thought of as evolving forward in time, normally from some fixed initial time, and the integral representation of a solution, involving as ...

advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. compared with numerical solutions, the analytical solutions benefit from some advantages. as such, many analytical solutions have been presented for the advection-diffusion equation. the difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...