Khilkova L. O.
Ukr. Mat. Zh. - 2019. - 71, № 5. - pp. 692-705
UDC 517.95, 519.21
We consider a boundary-value problem for the equation of stationary diffusion in a porous medium filled with small ball inclusions with absorbing surfaces. Absorption is described by a Robin’s nonlinear boundary condition. The locations and radii of the inclusions are randomly distributed and described by a set of finite-dimensional distribution functions. We study the asymptotic behavior of solutions to the problem when the number of balls increases and their radii decrease. We derive a homogenized equation for the main term of the asymptotics, and determine sufficient conditions for the distribution functions under which the solutions converge to the solutions of the homogenized problem in probability.
Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1201-1216
We consider a boundary-value problem used to describe the process of stationary diffusion in a porous medium with nonlinear absorption on the boundary. We study the asymptotic behavior of the solution when the medium becomes more and more porous and denser located in a bounded domain $Q$. A homogenized equation for the description of the main term of the asymptotic expansion is constructed.