Second critical exponent for a higher-order semilinear parabolic system
โ Scribed by Yang, ChunXiao; Yang, JinGe; Zheng, SiNing
- Book ID
- 125371830
- Publisher
- SP Science China Press
- Year
- 2014
- Tongue
- English
- Weight
- 188 KB
- Volume
- 58
- Category
- Article
- ISSN
- 1674-7283
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It is shown that there exists a critical exponent p \* > 1 for the bipolar blowup in the following sense. If 1 < p โค 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
We study solutions to the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the sense of Joseph and Lundgren and establish the rate of convergence to regular steady states. In the critical case, this rate contains a logarithmic term which does not appear in
In this paper, we consider the system q 1 1 0 0 and bounded. We prove that if pq F 1 every nonnegative solution is global. When ลฝ . ลฝ . ลฝ . ลฝ . pq ) 1 we let โฃ s p q 2 r2 pq y 1 , โค s 2 q q 1 r2 pq y 1 . We show that if ลฝ . ลฝ . max โฃ, โค ) Nr2 or max โฃ, โค s Nr2 and p, q G 1, then all nontrivial nonne