On a quasilinear parabolic–elliptic chemotaxis 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 priori bounds and global existence for a strongly coupled quasilinear parabolic system modeling chemotaxis
A priori bounds are found for solutions to a strongly coupled reactiondiffusion system that models competition of species in the presence of chemotaxis. These bounds are used to prove the existence of global solutions.
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 کاملBlow-up of Solutions to a Coupled Quasilinear Viscoelastic Wave System with Nonlinear Damping and Source
We study the blow-up of the solution to a quasilinear viscoelastic wave system coupled by nonlinear sources. The system is of homogeneous Dirichlet boundary condition. The nonlinear damping and source are added to the equations. We assume that the relaxation functions are non-negative non-increasing functions and the initial energy is negative. The competition relations among the nonlinear prin...
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: Journal of Differential Equations
سال: 2014
ISSN: 0022-0396
DOI: 10.1016/j.jde.2013.12.007