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Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gazzola, Filippo Grunau, Hans-Christoph |
| Copyright Year | 2007 |
| Abstract | We are interested in stability/instability of the zero steady state of the superlinear parabolic equation ut + Δ2u = |u|p-1u in $${\mathbb{R}^n\times[0,\infty)}$$ , where the exponent is considered in the “super-Fujita” range p > 1 + 4/n. We determine the corresponding limiting growth at infinity for the initial data giving rise to global bounded solutions. In the supercritical case p > (n + 4)/(n−4) this is related to the asymptotic behaviour of positive steady states, which the authors have recently studied. Moreover, it is shown that the solutions found for the parabolic problem decay to 0 at rate t−1/(p-1). |
| Starting Page | 389 |
| Ending Page | 415 |
| Page Count | 27 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00526-007-0096-7 |
| Volume Number | 30 |
| Alternate Webpage(s) | http://cvgmt.sns.it/papers/gazgru06/stability.pdf |
| Alternate Webpage(s) | http://www-ian.math.uni-magdeburg.de/home/grunau/papers/Supercritparabolic.pdf |
| Alternate Webpage(s) | http://www1.mate.polimi.it/~gazzola/stability.pdf |
| Alternate Webpage(s) | http://cvgmt.sns.it/media/doc/paper/1640/stability.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00526-007-0096-7 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
