由分数阶拉普拉斯算子控制的非线性狄利克雷边值问题的稳定性
Stability of nonlinear Dirichlet BVPs governed by fractional Laplacian.
作者信息
Bors Dorota
机构信息
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland.
出版信息
ScientificWorldJournal. 2014 Mar 2;2014:920537. doi: 10.1155/2014/920537. eCollection 2014.
Abstract
We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
摘要
我们考虑一类带有分数阶拉普拉斯算子和齐次狄利克雷边界数据的偏微分方程。陈述了所考虑方程的解连续依赖于参数的一些充分条件。给出了这些结果在一些最优控制问题中的应用。本文所应用的方法利用了问题的变分结构。
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