Traveling wave fronts in a delayed lattice competitive system

This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness.     

Modelling coupled water and heat transport in a soil–mulch–plant–atmosphere continuum (SMPAC) system

This paper presents a physically based model coupling water and heat transport in a soil–mulch–plant–atmosphere continuum (SMPAC) system, in which a transparent polyethylene mulch is applied to a winter wheat crop. The purpose of the study is to simulate profiles of soil water content and temperature for different stages of wheat growth. The mass and energy balance equations are constructed to determine upper boundary conditions of governing equations. Energy parameters are empirically formulated and calibrated from three-month field observed data. Resistance parameters in the SMPAC system are calculated. The mass and energy equations are solved by an iterative Newton–Raphson technique and a finite difference method is used to solve the governing equations. Water-consuming experiments are performed within the growing period of wheat. The results show that the model is quite satisfactory, particularly for high soil water content, in simulating the water and temperature profiles during the growth of the winter wheat.     

A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario

We study the weak solvability of a macroscopic, quasilinear reaction–diffusion system posed in a $2D$ porous medium which undergoes microstructural problems. The solid matrix of this porous medium is assumed to be made out of circles of not-necessarily uniform radius. The growth or shrinkage of these circles, which are governed by an ODE, has direct feedback to the macroscopic diffusivity via an additional elliptic cell problem.The reaction–diffusion system describes the macroscopic diffusion, aggregation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of this two-scale problem relies on a suitable application of Schauder’s fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.