A STRIKING CORRESPONDENCE BETWEEN THE DYNAMICS GENERATED BY THE VECTOR FIELDS AND BY THE SCALAR PARABOLIC EQUATIONS

Q4 Mathematics

Confluentes Mathematici Pub Date : 2010-05-11 DOI:10.1142/S1793744211000369

R. Joly, G. Raugel

引用次数: 7

Abstract

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations ẏ(t) = g(y(t)) on ℝd and those of the parabolic equations on a bounded domain Ω. We give details on the similarities of these dynamics in the cases d = 1, d = 2 and d ≥ 3 and in the corresponding cases Ω = (0, 1), Ω = 𝕋1 and dim(Ω) ≥ 2 respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations.

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由矢量场和标量抛物方程产生的动力学之间有惊人的对应关系

本文的目的是增强在有界域Ω上微分方程的动力学与在有界域上抛物方程的动力学之间的对应关系。在d = 1、d = 2和d≥3的情况下，以及相应的Ω =(0,1)、Ω =𝕋1和dim(Ω)≥2的情况下，详细说明了这些动力学的相似性。除了这种对应的美丽之外，这可以作为未来研究抛物方程动力学的指导方针。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.