退化动力系统的广义解

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI:10.1063/5.0144432

P. Jouan, U. Serres

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引用次数: 0

摘要

将退化动力系统A(x) =f(x)视为微分包含，研究了退化动力系统的解。集合Z={det(A(x))=0}，称为奇异集，假定其内部为空。详细地揭示了导致我们定义用于微分包含的集合的原因。然后，这个定义一方面应用于一般情况，另一方面应用于由物理学产生的特殊情况，这些情况可以在Saavedra, Troncoso和Zanelli中找到[J]。数学。物理学报，42(2001)。证明了广义解可以进入、离开或停留在奇异轨迹上。

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Generalized solutions to degenerate dynamical systems

The solutions to degenerate dynamical systems of the form A(x)ẋ=f(x) are studied by considering the equation as a differential inclusion. The set Z={det(A(x))=0}, called the singular set, is assumed to have an empty interior. The reasons leading us to the definition of the sets used for differential inclusion are exposed in detail. This definition is then applied on the one hand to generic cases and on the other hand to the particular cases resulting from physics, which can be found in Saavedra, Troncoso, and Zanelli [J. Math. Phys. 42, 4383 (2001)]. It is shown that generalized solutions may enter, leave, or remain in the singular locus.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.