Spectral aspects of regularization of the Cauchy problem for a degenerate equation

被引：0

作者：

V. Zh. Sakbaeva

机构：

[1] Moscow Institute of Physics and Technology,Department of Higher Mathematics

来源：

Proceedings of the Steklov Institute of Mathematics | 2008年 / 261卷

关键词：

Banach Space; Cauchy Problem; STEKLOV Institute; Linear Manifold; Contraction Semigroup;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the Cauchy problem for an equation whose generating operator is degenerate on some subset of the coordinate space. To approximate a solution of the degenerate problem by solutions of well-posed problems, we define a class of regularizations of the degenerate operator in terms of conditions on the spectral properties of approximating operators. We show that the behavior (convergence, compactness, and the set of partial limits in some topology) of the sequence of solutions of regularized problems is determined by the deficiency indices of the degenerate operator. We define an approximative solution of the degenerate problem as the limit of the sequence of solutions of regularized problems and analyze the dependence of the approximative solution on the choice of an admissible regularization.

引用

页码：253 / 261

页数：8

共 7 条

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[5] Sakbaev V. Zh.(2006)Degeneration and Regularization of the Operator in the Cauchy Problem for the Schrödinger Equation Sovrem. Mat. Prilozh. 38 95-109
[6] Sakbaev V. Zh.(2004)Functionals on Solutions of the Cauchy Problem for the Schrödinger Equation Degenerate on a Half-Line Zh. Vychisl. Mat. Mat. Fiz. 44 1654-1673
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