## Communicated by M. Renardy The steady-state problem of the non-linear reaction-diffusion system is considered. The existence of positive steady-solutions is established by using a fixed point theorem in ordered Banach space. The uniqueness of ordered positive steady-state solutions and an appl
Properties of Positive Solutions for Non-local Reaction–Diffusion Problems
✍ Scribed by Mingxin Wang; Yuanming Wang
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 604 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
In this paper we investigate the properties of positive solutions for three non-local reaction-diffusion problems. The conditions on the existence and non-existence of global positive solutions are given. Moreover, we prove that the blow-up set is the whole region when the non-linearity occurs in the equation.
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## Abstract We consider the non‐local singular boundary value problem where __q__ ∈ __C__^0^([0,1]) and __f__, __h__ ∈ __C__^0^((0,∞)), lim__f__(__x__)=−∞, lim__h__(__x__)=∞. We present conditions guaranteeing the existence of a solution __x__ ∈ __C__^1^([0,1]) ∩ __C__^2^((0,1]) which is positive
The system u 1t &2u 1 =u 1 u 2 &bu 1 , u 2t &2u 2 =au 1 in 0\_(0, T), where 0/R n is a smooth bounded domain, with homogeneous Dirichlet boundary conditions u 1 = u 2 =0 on 0\_(0, T) and initial conditions u 1 (x, 0), u 2 (x, 0), is studied. First, it is proved that there is at least one positive st