分层李群上的Fujita指数

IF 0.7 2区数学 Q2 MATHEMATICS

Collectanea Mathematica Pub Date : 2023-12-01 DOI:10.1007/s13348-023-00427-3

Durvudkhan Suragan, Bharat Talwar

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引用次数: 0

摘要

我们证明了在任意齐次维数q的分层李群上的半线性热方程\(\frac{Q}{Q-2}\)是Fujita指数，这涵盖了欧几里德情形，并对幂零李群的证明技术有了新的认识。我们研究的方程有一个强迫项，它只依赖于群元素，并且具有正积分。分层李群结构与测试函数法、Banach不动点定理在证明中起着重要的作用。

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Fujita exponent on stratified Lie groups

We prove that \(\frac{Q}{Q-2}\) is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension Q. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon the group elements and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.

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来源期刊

Collectanea Mathematica 数学-数学

CiteScore

2.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.