This article is cited in 1 paper

The solvability of the Cauchy problem for a class of Sobolev-type equations in tempered distributions

A. L. Pavlov<sup>ab

a</sup> Donetsk National University
^b Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine

Abstract: We give sufficient conditions for the existence of a solution to the Cauchy problem for the equation $P_2(D_x)\partial_t^2{u} + P_0(D_x) u = 0$ in the space of tempered distributions.

Keywords: Cauchy problem, Sobolev-type equation, tempered distribution, multiplier.

UDC: 517.955

MSC: 35R30

Received: 18.08.2021
Revised: 18.08.2021
Accepted: 15.06.2022

DOI: 10.33048/smzh.2022.63.513

 English version: Siberian Mathematical Journal, 2022, 63:5, 940–955