Kelvin–Voigt Equations with a Discontinuous Density Profile

• Published in: Journal of applied mechanics and technical physics Vol. 66; no. 1; pp. 89 - 99
• Main Authors: Antontsev, S. N., Kuznetsov, I. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.02.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Approximation; Cauchy problems; Classical and Continuum Physics; Classical Mechanics; Delta function; Density; Estimates; Fluid- and Aerodynamics; Inequality; Mass balance; Mathematical Modeling and Industrial Mathematics; Mechanical Engineering; Ordinary differential equations; Physics; Physics and Astronomy; Spacetime; Kelvin–Voigt equations; Dirac delta function, impulsive partial differential equation, initial layer, inhomogeneous incompressible fluid
• ISSN: 0021-8944; 1573-8620
• DOI: 10.1134/S0021894425010018

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.