Propagation of anisotropic Gabor singularities for Schrödinger type equations

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-04-02 DOI:10.1007/s00028-024-00963-w

引用次数: 0

Abstract

We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schrödinger type. The Hamiltonian is assumed to have a real-valued principal symbol with the anisotropic homogeneity \(a(\lambda x, \lambda ^\sigma \xi ) = \lambda ^{1+\sigma } a(x,\xi )\) for \(\lambda > 0\) where \(\sigma > 0\) is a rational anisotropy parameter. We prove that the propagator is continuous on anisotropic Shubin–Sobolev spaces. The main result says that the propagation of the anisotropic Gabor wave front set follows the Hamilton flow of the principal symbol.

查看原文本刊更多论文

薛定谔方程的各向异性 Gabor 奇点传播

摘要我们展示了各向异性 Gabor 波前集在一类薛定谔型演化方程的解中的传播结果。假定哈密顿有一个实值主符号，具有各向异性的同质性 \(a(\lambda x, \lambda ^\sigma \xi ) = \lambda ^{1+\sigma } a(x,\xi )\) for \(\lambda > 0\) 其中 \(\sigma > 0\) 是一个合理的各向异性参数。我们证明传播者在各向异性的舒宾-索博列夫空间上是连续的。主要结果表明，各向异性 Gabor 波前集的传播遵循主符号的汉密尔顿流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators