Long-term behaviour in a chemotaxis-fluid system with logistic source
نویسندگان
چکیده
منابع مشابه
Boundedness in a Three-dimensional Attraction-repulsion Chemotaxis System with Nonlinear Diffusion and Logistic Source
This article concerns the attraction-repulsion chemotaxis system with nonlinear diffusion and logistic source, ut = ∇ · ((u+ 1)m−1∇u)−∇ · (χu∇v) +∇ · (ξu∇w) + ru− μu , x ∈ Ω, t > 0, vt = ∆v + αu− βv, x ∈ Ω, t > 0, wt = ∆w + γu− δw, x ∈ Ω, t > 0 under Neumann boundary conditions in a bounded domain Ω ⊂ R3 with smooth boundary. We show that if the diffusion is strong enough or the logistic dampen...
متن کاملGlobal existence of classical solutions to a combined chemotaxis–haptotaxis model with logistic source
a r t i c l e i n f o a b s t r a c t This paper deals with a mathematical model of cancer invasion of tissue. The model consists of a system of reaction–diffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. In two space dimensions, we prove global existence and uniqueness of classical solutions to this model ...
متن کاملA Portable Chemotaxis Platform for Short and Long Term Analysis
Flow-based microfluidic systems have been widely utilized for cell migration studies given their ability to generate versatile and precisely defined chemical gradients and to permit direct visualization of migrating cells. Nonetheless, the general need for bulky peripherals such as mechanical pumps and tubing and the complicated setup procedures significantly limit the widespread use of these m...
متن کاملPattern Formation in Keller-Segel Chemotaxis Models with Logistic Growth
In this paper, we investigate the pattern formation in Keller–Segel chemotaxis over multi– dimensional bounded domains subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as chemoattraction rate χ increases. Then, using Crandall–Rabinowitz local theory with χ being the bifurcation parameter, we obtain the existence of no...
متن کاملA Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue (extracellular matrix, ECM). The model consists of a parabolic chemotaxis-haptotaxis PDE describing the evolution of cancer cell density, a parabolic PDE governing the evolution of matrix degrading enzyme concentration, and an ordinary differential equation reflecting the degradation of ECM. Following a recent appr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Models and Methods in Applied Sciences
سال: 2016
ISSN: 0218-2025,1793-6314
DOI: 10.1142/s021820251640008x