Diffusion in Composite Media with Close-to-touching Inclusions

Eric Bonnetier
University Joseph Fourier, Grenoble, France

ABSTRACT: Bonnetier and his colleagues study an integral formulation of a diffusion equation in a 2D composite medium containing inclusions with smooth boundaries, which can be close to touching. Their objective is to study the possible blow-up of the gradient of the field in terms of two parameters: the material coefficient contrast and the distance between the inclusions. They reformulate the problem via an integral representation and relate the behavior of the gradient to the spectral properties of the corresponding integral operator, the Neumann-Poincare operator, as these parameters degenerate.

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