Yu. V. Zasorin, “On the well-posedness of Cauchy problems for nonstationary equations with the unselected highest time derivative and the definition of the trace of distribution on the hyperplane of the initial data”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2021, Volume 191,Pages <nobr>47

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On the well-posedness of Cauchy problems for nonstationary equations with the unselected highest time derivative and the definition of the trace of distribution on the hyperplane of the initial data

Yu. V. Zasorin

Voronezh State University

Abstract: In this paper, we examine the well-posedness of Cauchy problems for nonstationary partial differential equations with nonselected highest time derivatives that have degeneration by these derivatives. For this purpose, we introduce the notion of the trace on the initial data hyperplane for distributions with semi-bounded supports, which allows one to establish some properties of the solution that ensure the well-posedness of the problems considered.

Keywords: nonstationary equation, unselected highest derivative, Cauchy problem, nonuniqueness, solution focusing, well-posedness, restriction, trace of distribution.

UDC: 517.956

MSC: 35J15

DOI: 10.36535/0233-6723-2021-191-47-73