论文标题
对基尔chhoff方程的解决方案的全球渐近行为
Global asymptotic behavior of solutions to a class of Kirchhoff equations
论文作者
论文摘要
在本文中，考虑了抛物线类型的Kirchhoff方程及其固定的对应物。对于进化问题，得出了弱溶液和相应能量功能的精确衰减速率。对于固定问题，通过应用Lagrange乘数法获得了基础解决方案。此外，还描述了一般全球解决方案的渐近行为。这些结果扩展了一些最新的结果，该结果在[具有任意初始能量，计算机和应用的任意初始能量，计算机和数学，75（2018），2018年，3283-3297]中获得的[全球和爆破解决方案的阈值结果]。
In this paper, a parabolic type Kirchhoff equation and its stationary counterpart are considered. For the evolution problem, the precise decay rates of the weak solution and of the corresponding energy functional are derived. For the stationary problem, a ground-state solution is obtained by applying Lagrange multiplier method. Moreover, the asymptotic behaviors of the general global solutions are also described. These results extend some recent ones obtained in [Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75(2018), 3283-3297] by Han and Li.
