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Existence of Positive Stationary Solutions and Threshold Results for a Reaction–Diffusion System

✍ Scribed by Yonggeng Gu; Mingxin Wang

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
453 KB
Volume
130
Category
Article
ISSN
0022-0396

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✦ Synopsis

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 stationary solution if 2 n<6. Second, it is proved that every positive stationary solution is a thereshold when 0 is a ball.

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✍ Hongwei Chen 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 245 KB 👁 2 views

## 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