The critical exponents for the quasi-linear parabolic equations with inhomogeneous terms
β Scribed by Xianzhong Zeng
- Book ID
- 108175781
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 189 KB
- Volume
- 332
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
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
It is shown that there exists a critical exponent p \* > 1 for the bipolar blowup in the following sense. If 1 < p β€ 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