Abstract
We study an adjoint initial-boundary value problem for linear parabolic equations; which arises when modeling the unidirectional motion of two viscous fluids with a common interface under the action of a pressure gradient. Under some conditions on the pressure gradient, we obtain a priori estimates and show that the solution enters a stationary mode. For semibounded layers, we find the solution in closed form and indicate the case of a self-similar solution. We determine the volume flow rates in the layers.
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Original Russian Text © V.K. Andreev, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 12, pp. 1667–1673.
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Andreev, V.K. On an adjoint initial-boundary value problem. Diff Equat 44, 1730–1736 (2008). https://doi.org/10.1134/S0012266108120094
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DOI: https://doi.org/10.1134/S0012266108120094