Results 81 to 90 of about 1,301 (120)

Mathematical models of cell self-organization

Journal of the Egyptian Mathematical Society, 2011
Various classes of Partial Differential Equations have shown to be successful in describing the self-organization of bacterial colonies, a topic also sometimes called socio-biology. For instance parabolic systems are standard; the classical Patlak–Keller–
Benoît Perthame
doaj   +1 more source

Variational–hemivariational system for contaminant convection–reaction–diffusion model of recovered fracturing fluid

Advances in Nonlinear Analysis
This work is devoted to study the convection–reaction–diffusion behavior of contaminant in the recovered fracturing fluid which flows in the wellbore from shale gas reservoir. First, we apply various constitutive laws for generalized non-Newtonian fluids,
Cen Jinxia, Migórski Stanisław, Yao Jen-Chih, Zeng Shengda   +3 more
doaj   +1 more source

Global boundedness in a two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity

Advances in Nonlinear Analysis
In this study, we investigate the two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity: ut=∇⋅(uθ−1∇u)−χ∇⋅uv∇v,x∈Ω,t>0,vt=Δv−v+u+g(x,t),x∈Ω,t>0,(∗)\left\{\begin{array}{ll}{u}_{t}=\nabla \cdot \left({u}^{\theta -1}\nabla u ...
Ren Guoqiang, Zhou Xing
doaj   +1 more source

Qualitative analysis of a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity

Infectious Disease Modelling, 2023
In this paper, a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity in a spatially heterogeneous environment is proposed. The well-posedness of the solution is firstly established. Then the basic reproduction number
Jianpeng Wang, Zhidong Teng, Binxiang Dai   +2 more
doaj  

Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy [PDF]

arXiv, 2017
In this paper we will apply the modified potential well method and variational method to the study of the long time behaviors of solutions to a class of parabolic equation of Kirchhoff type. Global existence and blow up in finite time of solutions will be obtained for arbitrary initial energy.
arxiv  

Computational dynamics of predator-prey model with the power-law kernel

Results in Physics, 2021
Evolution system which contains fractional derivatives can give rise to useful mathematical model for describing some important real-life or physical scenarios.
Kolade M. Owolabi
doaj  

A remark on reaction-diffusion equations in unbounded domains [PDF]

arXiv, 2002
We prove the existence of a compact L^2-H^1 attractor for a reaction-diffusion equation in R^n. This improves a previous result of B. Wang concerning the existence of a compact L^2-L^2 attractor for the same equation.
arxiv  

Boundary fluxes for non-local diffusion [PDF]

arXiv, 2006
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle.
arxiv  

The impact factors of the risk index and diffusive dynamics of a SIS free boundary model

Infectious Disease Modelling, 2022
To discuss the impact factors on the spread of infectious diseases, we study a free boundary problem describing a SIS (susceptible-infected-susceptible) model in a heterogeneous environment.
Yachun Tong, Inkyung Ahn, Zhigui Lin
doaj  

On a class of PDEs with nonlinear distributed in space and time state-dependent delay term [PDF]

arXiv, 2006
A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state-dependent delay and discuss advantages of this class.
arxiv