Andrey Amosov

Boundary value problem for radiation transfer equation in multilayered medium with reflection and refraction conditions

We consider a boundary value problem for the radiation transfer equation with reflection and refraction conditions describing a stationary process of the radiation transfer in multilayered semitransparent for radiation medium, consisting of m parallel vertical layers. We establish the existence and uniqueness of a solution for the problem with data from the spaces of type, . We also obtain a priori estimates for the solution.

Homogenization of a thermo-chemo-viscoelastic Kelvin-Voigt model

The paper is devoted to a model for the procedure of formation of a composite material constituted of solid fibers and of a solidifying matrix. The solidification process for the matrix depends on the temperature and on the degree of cure, which are used for the modeling of the mechanical properties of the matrix. Namely, the mechanical properties are described by Kelvin-Voigt viscoelastic equation with rapidly oscillating periodic coefficients depending on the temperature and the degree of cure. The latter are in turn solutions of a thermo-chemical problem with rapidly varying coefficients. We prove an error estimate for approximation of the viscoelastic problem by the same equation but with the coefficients depending on solution to the homogenized thermo-chemical problem. This estimate, in combination with our recent estimates for the viscoelastic (with time-dependent coefficients) and thermo-chemical homogenization problems, generates the overall error bound for the asymptotic solution to the full coup...

On two-scale homogenized equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth data

Abstract We study the initial-boundary value problem for a system of quasilinear equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth coefficients and initial data. We rigorously justify the passage to the corresponding limit initial-boundary value problem for a system of two-scale homogenized integro-differential equations, including the existence theorem for the limit problem. The results are global with respect to the time interval and the data.

Homogenization of the Integro-Differential Burgers Equation

The Burgers equation is a fundamental partial differential equation of fluid mechanics and acoustics. It occurs in various areas of applied mathematics, such as the modeling of gas dynamics and traffic flow (see [Ho50] and [Co51]).