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.

中文翻译：

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论Barenblatt-Zeldovich 中级渐近论

摘要

GN Barenblatt 和 Ya.B 引入了用于求解具有初始数据的演化方程以及在没有初始条件的情况下获得的相关解的中间渐近概念。泽尔多维奇在统计物理学和量子力学中扩展了严格决定论的概念。这里，根据 VP Maslov 的说法，为了使数学理论公理化，我们需要知道问题的初始数据满足的条件。我们证明了巴纳赫空间中分数阶微分方程没有初始条件的问题的正确可解性是中间渐近的必要但不是充分条件。给出了中间渐进的例子。