Қарағанды университетінің хабаршысы. Математика сериясы (Dec 2021)
On One Initial Boundary Value Problem for the Burgers Equation in a Rectangular Domain
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.
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