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

A. L. Pavlov<sup>ab

a</sup> Donetsk State University, Donetsk, Russia
^b Institute of Applied Mathematics and Mechanics, Donetsk, Russia

Abstract: We present sufficient conditions for the existence of a solution to the Cauchy problem for second-order linear homogeneous Sobolev-type equations with constant coefficients in the space of tempered distributions.

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

UDC: 517.951

MSC: 35R30

Received: 05.01.2025
Revised: 05.01.2025
Accepted: 25.04.2025

DOI: 10.33048/smzh.2025.66.412

 English version: Siberian Mathematical Journal, 2025, 66:4, 1017–1030