CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
نویسندگان
چکیده
منابع مشابه
Cross Diffusion Preventing Blow-Up in the Two-Dimensional Keller-Segel Model
Abstract. A (Patlak-) Keller-Segel model in two space dimensions with an additional crossdiffusion term in the equation for the chemical signal is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical substance. This allows one to prove, for arbitrarily small cross diffusion, the global existence of ...
متن کاملClassification of blow-up with nonlinear diffusion and localized reaction
We study the behaviour of nonnegative solutions of the reaction-diffusion equation ut = (u)xx + a(x)up in R× (0, T ), u(x, 0) = u0(x) in R. The model contains a porous medium diffusion term with exponent m > 1, and a localized reaction a(x)up where p > 0 and a(x) ≥ 0 is a compactly supported function. We investigate the existence and behaviour of the solutions of this problem in dependenc...
متن کاملBlow-up dynamics for the aggregation equation with degenerate diffusion
We study radially symmetric finite time blow-up dynamics for the aggregation equation with degenerate diffusion ut = ∆u m − ∇ · (u ∗ ∇(K ∗ u)) in R, where the kernel K(x) is of power-law form |x|−γ . Depending on m, d, γ and the initial data, the solution exhibits three kinds of blow-up behavior: self-similar with no mass concentrated at the core, imploding shock solution and near-self-similar ...
متن کاملSelf-similar blow-up for a diffusion–attraction problem
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see, e.g., Brenner M P et al 1999 Nonline...
متن کاملBlow up versus Global Boundedness of Solutions of Reaction Diffusion Equations with Nonlinear Boundary Conditions∗
In this paper we analyze the behavior of solutions of reaction-diffusion equations with nonlinear boundary conditions of the type (1.1). We show that if f(x, u) = −β0u and g(x, u) = uq in a neighborhood of a point x0 ∈ ΓN , then i) for the case q > 1, if p + 1 < 2q or if p + 1 = 2q and β0 < q, then blow up in finite time at x0 occurs. ii) for the case p > 1 if p + 1 > 2q or if p + 1 = 2q and β0...
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: 2012
ISSN: 0218-2025,1793-6314
DOI: 10.1142/s0218202512500418