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 . We show that the problem has solutions for small enough and we investigate the dependence of a specific family of solutions upon . By adopting a functional analytic approach we prove that the map which takes 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.
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| Riccardo Molinarolo |
Department of Mathematics, IMPACS
Aberystwyth University, Aberystwyth
Ceredigion SY23 3BZ, UK
email: email@example.com, firstname.lastname@example.org
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