Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay
Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay
复制标题
涉及具有最佳慢衰减初始数据的双调和算子的超线性抛物型方程的全局解
DOI：
10.1007/s00526-007-0096-7
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发表时间：
2007
影响因子：
2.1
通讯作者：
H. Grunau
中科院分区：
文献类型：
--
作者：
F. Gazzola;H. Grunau
本文研究了一类超线性抛物方程ut + Δ2u =| u| p-1u在$${\mathbb{R}^n\times[0，\infty）}$$中，其中指数被认为是在“超藤田”范围p > 1 + 4/n中。我们确定相应的极限增长在无穷大的初始数据产生的全球有界的解决方案。在超临界情况下p >（n + 4）/（n−4），这与作者最近研究的正稳态的渐近行为有关。此外，还证明了抛物问题的解以t−1/（p-1）的速率衰减到0。
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).