On One Initial Boundary Value Problem for the Burgers Equation in a Rectangular Domain

Muvasharkhan Jenaliyev, Madi Yergaliyev, A.A. Assetov, A.K. Kalibekova

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021

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DOI 10.31489/2021m4/74-88

Data confidence 70 medium

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Abstract

We consider some initial boundary value problems for the Burgers equation in a rectangular domain, which in a sense can be taken as a model one. The fact is that such a problem often arises when studying the Burgers equation in domains with moving boundaries. Using the methods of functional analysis, priori estimates, and Faedo-Galerkin in Sobolev spaces and in a rectangular domain, we show the correctness of the initial boundary value problem for the Burgers equation with nonlinear boundary conditions of the Neumann type.