A nonlocal boundary-value problem for partial differential equations of infinite order
01 Jan 1984-Ukrainian Mathematical Journal (Kluwer Academic Publishers-Plenum Publishers)-Vol. 35, Iss: 4, pp 420-423
About: This article is published in Ukrainian Mathematical Journal.The article was published on 1984-01-01. It has received 5 citations till now. The article focuses on the topics: Free boundary problem & Boundary value problem.
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TL;DR: In this article, the solvability of the problem for a nonhomogeneous partial differential equation of the second order in time and, generally, of the infinite order in the spatial variables with local conditions two-point in time in the classes of entire functions is studied.
Abstract: The solvability of the problem for a nonhomogeneous partial differential equation of the second order in time and, generally, of the infinite order in the spatial variables with local conditions two-point in time in the classes of entire functions is studied. In the case of unique solvability of the problem, a differential-symbol method of construction of its unique solution is proposed. In the case of nonunique solvability of the problem, we construct a partial solution.
13 citations
01 Feb 2019
TL;DR: In this article, the authors consider the problem of comparison of scalar products in real linear spaces and specify necessary and sufficient conditions for such comparison, which are easy to check and are typical for general theory of partial differential equations, including local multipoint problems.
Abstract: We consider the problem of comparison of scalar products in real linear spaces. Such problem arise during synthesis and optimal choosing of discrete and continuous measurement systems and combinatorial systems. Besides, they are also typical for general theory of partial differential equations, including local multipoint problems, whose solutions describe various oscillations and other natural processes. We specify necessary and sufficient conditions for such comparison, which are easy to check. We use special transformations of sums and series, which arise in respective scalar products, for finite- and infinite-dimensional cases.
4 citations
TL;DR: In this article, the conditions of well-posedness of nonlocal boundary-value problems are established for a second-order linear partial differential equation in an unbounded strip in the case where the real parts of the roots of its characteristic equation are different and nonzero.
Abstract: The conditions of well-posedness of nonlocal boundary-value problems are established for a second-order linear partial differential equation in an unbounded strip in the case where the real parts of the roots of its characteristic equation are different and nonzero.
3 citations
TL;DR: In this article, the authors studied the problem of Shilov parabolic equations of arbitrary order with constant coefficients with conditions nonlocal in time and periodic in space variables and established conditions for the existence and uniqueness of a classical solution of the problem.
Abstract: We study the problem for Shilov parabolic equations of arbitrary order with constant coefficients with conditions nonlocal in time and periodic in space variables. We establish conditions for the existence and uniqueness of a classical solution of the problem and prove metric theorems on lower bounds of small denominators appearing in the construction of a solution of the problem.
2 citations
30 Dec 2019
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TL;DR: In this article, the theory of nonlinear elliptic and parabolic equations of any order including equations of infinite order has been studied, and results of recent years have been presented on the theoretical analysis of these equations.
Abstract: Results of recent years are presented on the theory of nonlinear elliptic and parabolic equations of any order including equations of infinite order.
68 citations