On intermediate asymptotics Barenblatt–Zeldovich

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.