Open AccessThe Cauchy problem for inhomogeneous parabolic Shilov equations
Author(s) -
Iryna M. Dovzhytska
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.2.475-484
Subject(s) - mathematics , smoothness , initial value problem , cauchy problem , bounded function , parabolic partial differential equation , cauchy distribution , mathematical analysis , variable (mathematics) , class (philosophy) , partial differential equation , computer science , artificial intelligence
In this paper, we consider the Cauchy problem for parabolic Shilov equations with continuous bounded coefficients. In these equations, the inhomogeneities are continuous exponentially decreasing functions, which have a certain degree of smoothness by the spatial variable. The properties of the fundamental solution of this problem are described without using the kind of equation. The corresponding volume potential, which is a partial solution of the original equation, is investigated. For this Cauchy problem the correct solvability in the class of generalized initial data, which are the Gelfand and Shilov distributions, is determined.