Results 31 to 40 of about 908 (126)

Analysis of a mathematical model for the growth of cancer cells

, 2012
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or cell dead.
Kohlmann, Martin
core   +1 more source

Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks

Advances in Nonlinear Analysis
The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the ...
Li Bin
doaj   +1 more source

An Energetic Variational Approach for ion transport

, 2014
The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system.
Liu, Chun, Sheng, Ping, Xu, Shixin
core   +2 more sources

Critical mass for a no-flux-Dirichlet chemotaxis model with indirect signal production mechanism

Advances in Nonlinear Analysis
In this paper, we investigate the no-flux-Dirichlet parabolic–elliptic–ODE system with indirect signal production mechanismut*=Δu*−∇⋅u*∇v*,x∈Ω,t>0,0=Δv*−kv*+w*,x∈Ω,t>0,τ*wt*=−δw*+u*,x∈Ω,t>0,∂u*∂ν−u*∂v*∂ν=v*=0,x∈∂Ω,t>0,u*(x,0)=u0*(x),w*(x,0)=w0*(x),x∈Ω, $$
Yang Lan
doaj   +1 more source

Global-in-time behavior of the solution to a Gierer-Meinhardt system [PDF]

, 2012
Gierer-Meinhardt system is a mathematical model to describe biological pattern formation due to activator and inhibitor. Turing pattern is expected in the presence of local self-enhancement and long-range inhibition.
Karali, Georgia D, Suzuki, Takashi, Yamada, Yoshio   +2 more
core  

Boundedness and exponential convergence of a chemotaxis model for tumor invasion

, 2016
We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),& x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega, t>0,\\ z_t=\Delta z-z+u, & x\in\Omega,
Jin, Haiyang, Xiang, Tian
core   +1 more source

Protection Zones in Periodic-Parabolic Problems

Advanced Nonlinear Studies, 2020
This paper characterizes whether or ...
López-Gómez Julián
doaj   +1 more source

Asymptotic behavior of global mild solutions to the Keller-Segel-Navier-Stokes system in Lorentz spaces

Advances in Nonlinear Analysis
The Keller-Segel-Navier-Stokes system in RN{{\mathbb{R}}}^{N} is considered, where N≥3N\ge 3. We show the existence and uniqueness of local mild solutions for arbitrary initial data and gravitational potential in scaling invariant Lorentz spaces ...
Takeuchi Taiki
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The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in L1

Advances in Nonlinear Analysis, 2019
In bounded n-dimensional domains Ω, the Neumann problem for the parabolic ...
Winkler Michael
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Global boundedness and stability of a quasilinear two-species chemotaxis-competition model with nonlinear sensitivities

Advances in Nonlinear Analysis
This study deals with the global boundedness of a classical solution to a quasilinear two-species chemotaxis-competition model with nonlinear sensitivities in n≤3n\le 3. Due to the presence of nonlinear sensitivities, obtaining the necessary ‖w‖L∞\Vert w{
Yan Dongze, Liu Changchun
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