On Barenblatt–Zeldovich Intermediate Asymptotics

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-03-14 DOI:10.1134/s1064562423701351

V. A. Kostin, D. V. Kostin, A. V. Kostin

引用次数: 0

Abstract

The concept of intermediate asymptotics for the solution of an evolution equation with initial data and a related solution obtained without initial conditions was introduced by G.N. Barenblatt and Ya.B. Zeldovich in the context of extending the concept of strict determinism in statistical physics and quantum mechanics. Here, according to V.P. Maslov, to axiomatize the mathematical theory, we need to know the conditions satisfied by the initial data of the problem. We show that the correct solvability of a problem without initial conditions for fractional differential equations in a Banach space is a necessary, but not sufficient, condition for intermediate asymptotics. Examples of intermediate asymptotics are given.

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论巴伦布拉特-塞尔多维奇中间渐近线

摘要 G.N. Barenblatt 和 Ya.B. Zeldovich 在扩展统计物理学和量子力学中的严格确定性概念时，提出了有初始数据的演化方程解和无初始条件的相关解的中间渐近概念。在这里，根据 V.P. Maslov 的观点，为了使数学理论公理化，我们需要知道问题的初始数据所满足的条件。我们证明，巴拿赫空间中分数微分方程无初始条件问题的正确可解性是中间渐近的必要条件，但不是充分条件。我们给出了中间渐近的例子。

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

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.