Blowup Estimates for a Semilinear Reaction Diffusion System
✍ Scribed by Mingxin Wang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 73 KB
- Volume
- 257
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
This paper deals with the blowup estimates of positive solutions for a semilinear reaction diffusion system u t = u + u α v p , v t = v + u q v β , with null Dirichlet boundary conditions. The upper and lower bounds of blowup rates are obtained.
📜 SIMILAR VOLUMES
## Abstract In this paper, some sufficient conditions under which the quasilinear elliptic system ‐div(∣∇__~u~__∣__^p‐2^__∇__~u~__) = __u____v__, ‐div(∣∇__~u~__∣__^q‐2^__∇__~u~__) = __u____v__ in ℝ^N^(__N__≥3) has no radially symmetric positive solution is derived. Then by using this non‐existence
It is shown that there exists a critical exponent p \* > 1 for the bipolar blowup in the following sense. If 1 < p ≤ p \* , then there exist arbitrarily small initial data such that the solution exhibits the bipolar blowup, whereas if p > p \* , then the bipolar blowup does not occur for any suffici