Electron. J. Differential Equations, Vol. 2019 (2019), No. 53, pp. 1-29.

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

Riccardo Molinarolo

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 $\epsilon$. We show that the problem has solutions for $\epsilon$ small enough and we investigate the dependence of a specific family of solutions upon $\epsilon$. By adopting a functional analytic approach we prove that the map which takes $\epsilon$ to (suitable restrictions of) the corresponding solution can be represented in terms of real analytic functions.

Submitted May 8, 2018. Published April 22, 2019.
Math Subject Classifications: 35J25, 31B10, 45A05, 35B25, 35C20.
Key Words: Nonlinear non-autonomous transmission problem; singularly perturbed perforated domain; small inclusion; Laplace operator; real analytic continuation in Banach space; asymptotic behaviour.

Show me the PDF file (435 KB), TEX file for this article.

Riccardo Molinarolo
Department of Mathematics, IMPACS
Aberystwyth University, Aberystwyth
Ceredigion SY23 3BZ, UK
email: rim22@aber.ac.uk, ricmolinarolo@gmail.com

Return to the EJDE web page