Singular Behavior of Electric Field of High-Contrast Concentrated Composites
Yuliya Gorb · Multiscale Modeling and Simulation · 2015
A heterogeneous conduction medium of constituents with vastly different electrical properties, whose inhomogeneities are in close proximity to each other, is considered. The mathematical formulation consists of the Dirichlet problem for the conductivity equation with a nonuniformly elliptic operator and discontinuous coefficients. The gradient of the solution to the corresponding problem exhibits singular behavior (blowup) with respect to the distance between inhomogeneities. This paper introduces a concise procedure for capturing the leading term of that blowup precisely. The developed approach is based on thorough study of the system's energy. The introduced methodology allows for a number of generalizations.