scholarly journals Regularity, Asymptotic Solutions and Travelling Waves analysis in a porous medium system to model the interaction between invasive and invaded species

2021 ◽  
Author(s):  
José Díaz ◽  
Antonio Naranjo
Keyword(s):  
Porous Medium ◽  
Travelling Waves ◽  
Stationary Solutions ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Diffusion Parameters ◽  
Medium System ◽  
Topological Argument ◽  
And Diffusion ◽  
Stable Connection

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the selfsimilar structure that permits to show the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive specie predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded specie TW is not trivial in the non-linear diffusion case and reflects the existence of a TW trajectory governed by the invaded specie runaway (in the direction of the advection) and the diffusion (acting along a finite speed front or support).

scholarly journals Existence, uniqueness and travelling waves to model an invasive specie interaction with heterogeneous reaction and non-linear diffusion

2022 ◽  
Vol 7 (4) ◽  
pp. 5768-5789
Author(s):  
José L. Díaz ◽  
Keyword(s):  
Heterogeneous Reaction ◽  
Travelling Waves ◽  
Type Equation ◽  
Mathematical Treatment ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Finite Speed ◽  
Non Linear ◽  
Medium Type ◽  
Stable Connection

<abstract><p>It is the objective to provide a mathematical treatment of a model to predict the behaviour of an invasive specie proliferating in a domain, but with a certain hostile zone. The behaviour of the invasive is modelled in the frame of a non-linear diffusion (of Porous Medium type) equation with non-Lipschitz and heterogeneous reaction. First of all, the paper examines the existence and uniqueness of solutions together with a comparison principle. Once the regularity principles are shown, the solutions are studied within the Travelling Waves (TW) domain together with stability analysis in the frame of the Geometric Perturbation Theory (GPT). As a remarkable finding, the obtained TW profile follows a potential law in the stable connection that converges to the stationary solution. Such potential law suggests that the pressure induced by the invasive over the hostile area increases over time. Nonetheless, the finite speed, induced by the non-linear diffusion, slows down a possible violent invasion.</p></abstract>

scholarly journals Ergodic control of diffusions with random intervention times

2021 ◽  
Vol 58 (1) ◽  
pp. 1-21
Author(s):  
Harto Saarinen ◽  
Jukka Lempa
Keyword(s):  
Optimal Solution ◽  
Singular Control ◽  
Control Policy ◽  
Control Problems ◽  
Ergodic Control ◽  
Linear Diffusion ◽  
One Dimensional ◽  
And Diffusion ◽  
Independent Poisson Process ◽  
Exact Amount

AbstractWe study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

scholarly journals Effect of chemical reaction and radiation on double diffusive flow of a viscous, dissipative fluid through porous medium in a rectangular cavity with heat sources

2013 ◽  
Vol 18 (4) ◽  
pp. 1115-1150
Author(s):  
T.L. Raju ◽  
P. Muralidhar
Keyword(s):  
Porous Medium ◽  
Stream Function ◽  
Rectangular Cavity ◽  
Heat Sources ◽  
Element Analysis ◽  
Coupled Equations ◽  
Stiffness Matrices ◽  
Diffusive Flow ◽  
Transfer Flow ◽  
And Diffusion

Abstract In this paper, an attempt is made to discuss the combined influence of radiation and dissipation on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular cavity using the Darcy model. Making use of the incompressibility, the governing non-linear coupled equations for the momentum, energy and diffusion are derived in terms of the non-dimensional stream function, temperature and concentration. The Galerkin finite element analysis with linear triangular elements is used to obtain the global stiffness matrices for the values of stream function, temperature and concentration. These coupled matrices are solved using an iterative procedure and expressions for the stream function, temperature and concentration are obtained as linear combinations of the shape functions. The behavior of temperature, concentration, the Nusselt number and Sherwood number is discussed computationally for different values of the governing parameters, such as the Rayleigh Number (Ra), heat source parameter (α), Eckert number (Ec), Schmidt Number (Sc), Soret parameter (S0), buoyancy ratio (N).

scholarly journals On FTCS Approach for Box Model of Three-Dimension Advection-Diffusion Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Jeffry Kusuma ◽  
Agustinus Ribal ◽  
Andi Galsan Mahie
Keyword(s):  
Mathematical Model ◽  
Three Dimension ◽  
Sand Mining ◽  
Mining Pollution ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Diffusion Parameters ◽  
Sea Sand ◽  
And Diffusion ◽  
Pollution Distribution

This paper describes a numerical solution for mathematical model of the transport equation in a simple rectangular box domain. The model of street tunnel pollution distribution using two-dimension advection and three-dimension diffusion is solved numerically. Because of the nature of the problem, the model is extended to become three-dimension advection and three-dimension diffusion to study the sea-sand mining pollution distribution. This model with various advection and diffusion parameters and the boundaries conditions is also solved numerically using a finite difference (FTCS) method.

scholarly journals Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation

2020 ◽  
Vol 30 (11) ◽  
pp. 2105-2137
Author(s):  
Nancy Rodríguez ◽  
Michael Winkler
Keyword(s):  
Porous Medium ◽  
Initial Data ◽  
Criminal Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Urban Crime ◽  
Source Terms ◽  
Linear Diffusion ◽  
Macroscopic Models ◽  
Smoothing Effects

We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Ref. 29 [M. B. Short, M. R. D’Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18 (2008) 1249–1267]. The focus here is on the question of how far a certain porous medium enhancement in the random diffusion of criminal agents may exert visible relaxation effects. It is shown that sufficient regularity of the non-negative source terms in the system and a sufficiently strong nonlinear enhancement ensure that a corresponding Neumann-type initial–boundary value problem, posed in a smoothly bounded planar convex domain, admits locally bounded solutions for a wide class of arbitrary initial data. Furthermore, this solution is globally bounded under mild additional conditions on the source terms. These results are supplemented by numerical evidence which illustrates smoothing effects in solutions with sharply structured initial data in the presence of such porous medium-type diffusion and support the existence of singular structures in the linear diffusion case, which is the type of diffusion proposed in Ref. 29.

Determination of sorption and diffusion parameters of 99Tc in crushed granite using through-diffusion experiments

2016 ◽  
Vol 311 (2) ◽  
pp. 1111-1116 ◽  
Author(s):  
Yu-Hung Shih ◽  
Tsuey-Lin Tsai ◽  
Liang-Cheng Chen ◽  
Te-Yen Su ◽  
Chuan-Pin Lee ◽  
...  
Keyword(s):  
Diffusion Parameters ◽  
Crushed Granite ◽  
Through Diffusion ◽  
And Diffusion
Sign in / Sign up

Export Citation Format

Share Document