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We consider the homogenization of a parabolic problem in a perforated domain with Robin–Neumann boundary conditions oscillating in time. Such oscillations must compensate the blow up of the boundary measure of the holes. We use the technique of time-periodic unfolding in order to obtain a macroscopic parabolic problem containing an extra linear term due to the absorption determined by the Robin condition. [ABSTRACT FROM AUTHOR]

Abstract: We study the existence and uniqueness of solutions to an elliptic problem with a nonlinear dynamic boundary condition, relating the conormal derivative of the unknown to the time derivative of its jump across an internal interface. We firstly prove the well-posedness of a suitable linear version of this problem, by means of a classical result in abstract parabolic theory; then, we study the nonlinear case using a fixed point technique. Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues. [Copyright &y& Elsevier]

We prove existence and homogenization results for a family of elliptic problems involving interfaces and a singular lower order term. These problems model heat or electrical conduction in composite media. [ABSTRACT FROM AUTHOR]