Jordan-Block型抛物型系统的拟线性微分约束

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-06-10 DOI:10.1111/sapm.70072

Alessandra Rizzo, Pierandrea Vergallo

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引用次数: 0

摘要

证明了线性退化性是Jordan-block型系统存在相容拟线性微分约束的必要条件。这个条件对于2 × 2$ 2\ × 2$系统也是充分的，并且与哈密顿性质等价。本文给出了抛物型方程组的若干显式解，并综合了由结合律理论产生的两个主要层次和硬杆情况下El’s方程的三角泛函化简。

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Quasilinear Differential Constraints for Parabolic Systems of Jordan-Block Type

We prove that linear degeneracy is a necessary conditions for systems in Jordan-block form to admit a compatible quasilinear differential constraint. Such condition is also sufficient for $2 \times 2$ systems and turns out to be equivalent to the Hamiltonian property. Some explicit solutions of parabolic systems are herein given: two principal hierarchies arising from the associativity theory and the delta-functional reduction of the El's equation in the hard rod case are integrated.

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.