Kelvin-Voigt Equations Characterized by Abruptly Changing Density
S. N. Antontsev1, I. V. Kuznetsov1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Altai State University, Barnaul, Russia
Keywords: Dirac delta function, impulse partial differential equation, initial layer, inhomogeneous incompressible fluid, Kelvin-Voigt equation
Abstract
Kelvin-Voigt equations for inhomogeneous fluids with a singular right side are studied. A singular term that approximates the Dirac delta function on an initially infinitely thin layer is introduced into the right side of a mass balance equation. This singular term is similar to the relaxation term used to describe nonequilibrium processes in hydrodynamics. In an extreme case, when a small parameter, namely the characteristic size of the initial layer, tends to zero, the density and velocity at the initial time change abruptly.
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