Search results for "transmission problem"
showing 3 items of 3 documents
Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem
2020
Abstract We consider the Laplace equation in a domain of R n , n ≥ 3 , with a small inclusion of size ϵ . On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.
Existence results for a nonlinear nonautonomous transmission problem via domain perturbation
2021
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.
Dependence of effective properties upon regular perturbations
2022
In this survey, we present some results on the behavior of effective properties in presence of perturbations of the geometric and physical parameters. We first consider the case of a Newtonian fluid flowing at low Reynolds numbers around a periodic array of cylinders. We show the results of [43], where it is proven that the average longitudinal flow depends real analytically upon perturbations of the periodicity structure and the cross section of the cylinders. Next, we turn to the effective conductivity of a periodic two-phase composite with ideal contact at the interface. The composite is obtained by introducing a periodic set of inclusions into an infinite homogeneous matrix made of a di…