In this paper we describe the asymptotic behavior of a problem depending on a small parameter ε>0 and modelling the stationary heat diffusion in a two-component conductor. The flow of heat is proportional to the jump of the temperature field, due to a contact resistance on the interface.More precisely, we give an homogenization result for the stationary heat equation with oscillating coefficients in a domain [Formula: see text] of ℝn, where [Formula: see text] is connected and [Formula: see text] is union of ε-periodic disconnected inclusions of size ε. These two sub-domains of Ω are separated by a contact surface Γε, on which we prescribe the continuity of the conormal derivatives and a jump of the solution proportional to the conormal derivative, by means of a function of order εγ.We describe the limit problem for γ>-1. The two cases -1<γ≤1 (Theorem 2.1) and γ>1 (Theorem 2.2) need to be treated separately, because of different a priori estimates.
In this paper we study the asymptotic behaviour of the
wave equation with
rapidly oscillating coefficients in a two-component composite with
ε-periodic imperfect inclusions.
We prescribe on the interface between the two components a jump of
the solution proportional to the conormal derivatives through a
function of order ε^γ. For the different values of
γ, we obtain different limit problems. In particular, for
γ=1 we have a linear memory effect in the homogenized
problem
We study the Dirichlet problem for linear elliptic second order partial differential equations with discontinuous coefficients in divergence form in unbounded domains. We establish an existence and uniqueness result and we prove an a priori bound in L p , p > 2. MSC: 35J25; 35B45; 35R05
We prove an L p -a priori bound, p > 2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.
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