On nonlinear processes involving population growth and diffusion

1967 ◽  
Vol 4 (2) ◽  
pp. 281-290 ◽  
Author(s):  
Elliott W. Montroll
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Population Growth ◽  
General Class ◽  
Diffusion Processes ◽  
Nonlinear Processes ◽  
Partial Differential ◽  
And Diffusion ◽  
Simultaneous Growth

A number of years ago, R. A. Fisher discussed the problem of the propagation of a virile mutant in a population. At about the same time, Kolmogorov, Petrovsky, and Piscounoff, whom we shall refer to as KPP, investigated a general class of partial differential equations which describe simultaneous growth and diffusion processes.

On nonlinear processes involving population growth and diffusion

1967 ◽  
Vol 4 (02) ◽  
pp. 281-290 ◽  
Author(s):  
Elliott W. Montroll
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Population Growth ◽  
General Class ◽  
Diffusion Processes ◽  
Nonlinear Processes ◽  
Partial Differential ◽  
And Diffusion ◽  
Simultaneous Growth

A number of years ago, R. A. Fisher discussed the problem of the propagation of a virile mutant in a population. At about the same time, Kolmogorov, Petrovsky, and Piscounoff, whom we shall refer to as KPP, investigated a general class of partial differential equations which describe simultaneous growth and diffusion processes.

scholarly journals Similarity Solutions of Partial Differential Equations in Probability

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Mario Lefebvre
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Processes ◽  
Separation Of Variables ◽  
Similarity Solutions ◽  
Two Dimensional ◽  
Partial Differential ◽  
Generalized Fourier Series ◽  
Dimensional Diffusion ◽  
Concentric Circles

Two-dimensional diffusion processes are considered between concentric circles and in angular sectors. The aim of the paper is to compute the probability that the process will hit a given part of the boundary of the stopping region first. The appropriate partial differential equations are solved explicitly by using the method of similarity solutions and the method of separation of variables. Some solutions are expressed as generalized Fourier series.

scholarly journals An Implementation Solution for Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nicolas Bertrand ◽  
Jocelyn Sabatier ◽  
Olivier Briat ◽  
Jean-Michel Vinassa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Differentiation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Diffusion Equations ◽  
Electrochemical Interfaces ◽  
And Diffusion

The link between fractional differentiation and diffusion equation is used in this paper to propose a solution for the implementation of fractional diffusion equations. These equations permit us to take into account species anomalous diffusion at electrochemical interfaces, thus permitting an accurate modeling of batteries, ultracapacitors, and fuel cells. However, fractional diffusion equations are not addressed in most commercial software dedicated to partial differential equations simulation. The proposed solution is evaluated in an example.

scholarly journals Stochastic Measure Diffusion Processes

1979 ◽  
Vol 22 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Donald A. Dawson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Diffusion Processes ◽  
Partial Differential ◽  
Stochastic Measure ◽  
Recent Developments

The purpose of this article is to give an introduction to the study of a class of stochastic partial differential equations and to give a brief review of some of the recent developments in this field. This study has evolved naturally out of the theory of stochastic differential equations initiated in a pioneering paper of K. Itô [13]. In order to set this review in its appropriate setting we begin by considering a simple scalar stochastic differential equation.

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