The Cauchy problem for inhomogeneous parabolic Shilov equations

Keywords: parabolic Shilov equation, fundamental solution, Cauchy problem, correct solvability, volume potential
Published online: 2021-10-17


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.

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How to Cite
DovzhytskaI. The Cauchy Problem for Inhomogeneous Parabolic Shilov Equations. Carpathian Math. Publ. 2021, 13, 475-484.