L2-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian
L2-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian
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涉及 Hessian 矩阵的四阶抛物线偏微分方程解的 L2 范数放大
DOI：
10.1016/j.jde.2018.06.015
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发表时间：
2018
影响因子：
2.4
通讯作者：
Jun Zhou
中科院分区：
文献类型：
--
作者：
Jun Zhou
本文讨论了晶体外延生长理论中的一个四阶抛物偏微分方程。我们专注于Escudero等人提出的一个开放性问题的研究。（2015）[4]，即Lp-范数爆破。当初始能量J（u 0）< λ 1 6 <$u0 <$2 2时，证明了解在有限时间内爆破，其中λ 1是双调和算子的最小Dirichlet特征值.此外，还得到了解的寿命，推广了Xu和Zhou（2017）[12]的结果.
This paper deals with a fourth order parabolic PDE arising in the theory of epitaxial growth of crystal. We focalize the study on one open question proposed by Escudero et al.(2015)[4], that is, L p-norm blow-up. For the initial energy J (u 0)< λ 1 6‖ u 0‖ 2 2, we prove the solution blows up in finite time with L 2-norm, where λ 1 is the least Dirichlet eigenvalue of the biharmonic operator. Moreover, the lifespan of the solution is got, and the results of this paper also generalize the results got by Xu and Zhou (2017)[12].