Global existence and blow-up for a system describing the aggregation of microglia
نویسندگان
چکیده
We consider the system u t = ∆u − ∇ · (χ u∇v) + ∇ · (ξ u∇w), τ v t = ∆v + αu − βv, τ w t = ∆w + γ u − δw, which has been proposed to describe the aggregation of microglia. We study the problem of global existence and blow-up for this system.
منابع مشابه
Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملGlobal existence, stability results and compact invariant sets for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$
We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$ is a positive function lying in $L^{N/2}(mathb...
متن کاملSUPER- AND SUB-ADDITIVE ENVELOPES OF AGGREGATION FUNCTIONS: INTERPLAY BETWEEN LOCAL AND GLOBAL PROPERTIES, AND APPROXIMATION
Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {it Fuzzy Sets and Systems} {bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with ...
متن کاملGlobal and blow-up solutions for a mutualistic model
We study the global and blow-up solutions for a strong degenerate reaction–diffusion system modeling the interactions of two biological species. The local existence and uniqueness of a classical solution are established. We further give the critical exponent for reaction and absorption terms for the existence of global and blow-up solutions. We show that the solution may blow up if the intraspe...
متن کاملA note on critical point and blow-up rates for singular and degenerate parabolic equations
In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 35 شماره
صفحات -
تاریخ انتشار 2014