具有快速对流的热方程:源型解和大时间行为

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI:10.3934/dcdss.2023182

Jørgen Endal, Liviu I. Ignat, Fernando Quirós

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引用次数: 0

摘要

在一定的尾部控制条件下，研究了快速对流热方程Cauchy问题源型解的存在唯一性。我们允许解的符号改变，但实际上我们会证明它们的符号和初始数据是一样的，初始数据是狄拉克函数的倍数。作为一个应用，我们得到了具有可积初始数据的非负有界解的大时间行为，涵盖了自上世纪末以来一直开放的几个维度的热方程。

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Heat equations with fast convection: Source-type solutions and large-time behaviour

We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the same sign as the initial data, which is a multiple of the Dirac delta. As an application, we obtain the large-time behaviour of nonnegative bounded solutions with integrable initial data to heat equations with fast convection, covering the case of several dimensions that remained open since the end of last century.

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来源期刊

Discrete and Continuous Dynamical Systems-Series S MATHEMATICS, APPLIED-

CiteScore

3.70

自引率

5.60%

发文量

177

期刊介绍： Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.