Asymptotic behavior of the solution of singularly perturbed transmission problems in a periodic domain | Zendy

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Asymptotic behavior of the solution of singularly perturbed transmission problems in a periodic domain

Author(s) -

Pukhtaievych Roman

Publication year - 2018

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4832

Subject(s) - mathematics , transmission (telecommunications) , domain (mathematical analysis) , nonlinear system , method of matched asymptotic expansions , mathematical analysis , ideal (ethics) , representation (politics) , set (abstract data type) , boundary value problem , computer science , telecommunications , philosophy , programming language , physics , epistemology , quantum mechanics , politics , political science , law

Summary This paper is devoted to the study of the asymptotic behavior of the solutions of singularly perturbed transmission problems in a periodically perforated domain. The domain is obtained by making in R n a periodic set of holes, each of them of size proportional to a positive parameter ε . We first consider an ideal transmission problem and investigate the behavior of the solution as ε tends to 0. In particular, we deduce a representation formula in terms of real analytic maps of ε and of some additional parameters. Then we apply such result to a nonideal nonlinear transmission problem.

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