Boundedness and finite-time blow-up in a quasilinear parabolic–elliptic chemotaxis system with logistic source and nonlinear production
نویسندگان
چکیده
This paper deals with the quasilinear parabolic–elliptic chemotaxis system logistic source and nonlinear production, { u t = ∇ ⋅ ( D ) − S v + λ μ κ , x ∈ Ω > 0 Δ M f ‾ where 1 : | ∫ d are functions generalizing prototypes m α ℓ R . In case Fuest (2021) [5] obtained conditions for such that solutions blow up in finite time. However, above boundedness finite-time blow-up of have been not yet established. gives under some
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 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 کاملFinite-time Blow-up in a Degenerate Chemotaxis System with Flux Limitation
This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by ( ) ⎧⎨ ⎩ ut = ∇ · ( u∇u √ u2 + |∇u|2 ) − χ∇ · ( u∇v √ 1 + |∇v|2 ) ,
متن کاملBlow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
and Applied Analysis 3 Mu et al. 19 studied the secondary critical exponent for the following p-Laplacian equation with slow decay initial values: ut div ( |∇u|p−2∇u ) u, x, t ∈ R × 0, T , u x, 0 u0 x , x ∈ R, 1.6 where p > 2, q > 1, and showed that, for q > q∗ c p − 1 p/N , there exists a secondary critical exponent ac p/ q 1 − p such that the solution u x, t of 1.6 blows up in finite time for...
متن کاملFinite time blow-up in nonlinear suspension bridge models
This paper settles a conjecture by Gazzola and Pavani [10] regarding solutions to the fourth order ODE w(4) + kw′′ + f (w) = 0 which arises in models of traveling waves in suspension bridges when k > 0. Under suitable assumptions on the nonlinearity f and initial data, we demonstrate blow-up in finite time. The case k ≤ 0 was first investigated by Gazzola et al., and it is also handled here wit...
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 Mathematical Analysis and Applications
سال: 2022
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2021.125654