Non-simultaneous blow-up for a reaction-diffusion system with absorption and coupled boundary flux
نویسندگان
چکیده
منابع مشابه
Non–simultaneous Blow–up for a Semilinear Parabolic System with Localized Reaction Terms
In this paper, we study positive blow-up solutions of the semilinear parabolic system with localized reactions ut = Δu+ vr + up(0,t), vt = Δv + us + vq(0,t) in the ball B = {x ∈ R N : |x| < R} , under the homogeneous Dirichlet boundary condition. It is shown that nonsimultaneous blow-up may occur according to the value of p , q , r , and s ( p,q,r,s > 1). We also investigate blow-up rates of al...
متن کاملBlow-up for a reaction-diffusion equation with variable coefficient
We study the blow-up behavior for positive solutions of a reaction–diffusion equationwith nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point. © 2012 Elsevier Ltd. All rights reserved.
متن کاملSimultaneous vs. Non-simultaneous Blow-up in Numerical Approximations of a Parabolic System with Nonlinear Boundary Conditions
We study the asymptotic behavior of a semidiscrete numerical approximation for a pair of heat equations ut = ∆u, vt = ∆v in Ω × (0, T ); fully coupled by the boundary conditions ∂u ∂η = up11vp12 , ∂v ∂η = up21vp22 on ∂Ω× (0, T ), where Ω is a bounded smooth domain in Rd. We focus in the existence or not of non-simultaneous blow-up for a semidiscrete approximation (U, V ). We prove that if U blo...
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 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: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2010
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2010.1.45