A. L. Pavlov, “The Cauchy problem for one equation of Sobolev type”, Mat. Tr., 2018, Volume 21, Number 1,Pages <nobr>125

This article is cited in 7 papers

The Cauchy problem for one equation of Sobolev type

A. L. Pavlov^ab

^a Donetsk National University, Donetsk, 283001 Ukraine
^b Insititute of Applied Mathematics and Mechanics, Donetsk, 283114 Ukraine

Abstract: We give necessary and sufficient conditions for the existence of a solution to the Cauchy problem for the equation $\Delta^k\partial^2_tu+(-1)^ku=0$ in the space of tempered distributions.

Key words: Cauchy problem, equation of Sobolev type, regularization of a distribution.

UDC: 517.955

Received: 12.05.2017

DOI: 10.17377/mattrudy.2018.21.106