Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem

Date

2019-04-22

Authors

Molinarolo, Riccardo

Journal Title

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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.

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Attribution 4.0 International

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