A. L. Pavlov, “Existence of solutions to the Cauchy problem for some class of Sobolev-type equations in the space of tempered distributions”, Sibirsk. Mat. Zh., 2019, Volume 60, Number 4,Pages <nobr>824

This article is cited in 3 papers

Existence of solutions to the Cauchy problem for some class of Sobolev-type equations in the space of tempered distributions

A. L. Pavlov^ab

^a Donetsk National University, Donetsk, Ukraine
^b Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine

Abstract: We give sufficient conditions for existence of a solution to the Cauchy problem for the equation $P_1(D_x) \partial_t u-P_0(D_x) u=0$ in the space of tempered distributions.

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

UDC: 517.955

Received: 03.11.2018
Revised: 03.11.2018
Accepted: 15.05.2019

DOI: 10.33048/smzh.2019.60.410