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The Dirichlet problem in an infinite layer for a system of differential equations with shifts

  • Zinovii Nytrebych , Roman Shevchuk EMAIL logo and Ivan Savka
Published/Copyright: December 13, 2023
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Abstract

In this paper, we study the problem with data on the boundary of the infinite layer

{ ( t , x ) : t ( 0 , h ) , x R s } , h > 0 , s N ,

for the system of two differential equations of the second order in the time variable 𝑡 with shifts in the spatial variables x 1 , x 2 , , x s . We propose a differential-symbol method of constructing a solution of the problem and identify a class of vector functions in which the obtained solution is unique. The method of solving the Dirichlet problem in the layer is illustrated by examples.

MSC 2010: 35G15

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Received: 2023-06-15
Revised: 2023-07-27
Accepted: 2023-07-31
Published Online: 2023-12-13
Published in Print: 2024-08-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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