Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem
Date
2019-04-22
Authors
Molinarolo, Riccardo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we analyze a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size ε. We show that the problem has solutions for ε small enough and we investigate the dependence of a specific family of solutions upon ε. By adopting a functional analytic approach we prove that the map which takes ε to (suitable restrictions of) the corresponding solution can be represented in terms of real analytic functions.
Description
Keywords
Nonlinear non-autonomous transmission problem, Singularly perturbed perforated domain, Small inclusion, Laplace operator, Real analytic continuation in Banach space, Asymptotic behaviour
Citation
Molinarolo, R. (2019). Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem. <i>Electronic Journal of Differential Equations, 2019</i>(53), pp. 1-29.
Rights
Attribution 4.0 International