This article is cited in 2 papers

MATHEMATICS

On intermediate asymptotics Barenblatt–Zeldovich

V. A. Kostin^a, D. V. Kostin^ab, A. V. Kostin<sup>a

a</sup> Voronezh State University, Voronezh, Russia
^b Voronezh State Pedagogical University, Воронеж, Россия

Abstract: The concept of “intermediate asymptotics” for solving an evolution equation with initial values data and the associated solution without initial conditions was introduced by G.N. Barenblatt and Y.B. Zeldovich in connection with the expansion of the concept of “strict determinism” in statistical physics and quantum mechanics. Here, according to V.P. Maslov, to axiomatize a mathematical theory, one must also know what conditions the initial solutions of the problem must satisfy. The paper shows that the correct solvability of the problem without initial conditions for fractional differential equations in a Banach space is necessary but not sufficient condition of “intermediate asymptotics”. Examples of “intermediate asymptotics” are given.

Keywords: intermediate asymptotics, well-posed problems, Cauchy problem, equations without initial conditions, strongly continuous semigroups, fractional powers of operators.

UDC: 517.9

Presented: V. P. Maslov
Received: 11.07.2023
Revised: 05.09.2023
Accepted: 18.10.2023

DOI: 10.31857/S2686954323600763

 English version: Doklady Mathematics, 2023, 108:3, 454–458

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