دورية أكاديمية
A singularly perturbed nonlinear traction problem in a periodically perforated domain: A functional analytic approach
| العنوان: | A singularly perturbed nonlinear traction problem in a periodically perforated domain: A functional analytic approach |
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| المؤلفون: | Dalla Riva M., Musolino P. |
| المساهمون: | Dalla Riva, M., Musolino, P. |
| سنة النشر: | 2014 |
| المجموعة: | Padua Research Archive (IRIS - Università degli Studi di Padova) |
| مصطلحات موضوعية: | integral representations, integral operators, integral equation method, linearized elastostatic, nonlinear boundary value problems for linear elliptic equation, periodically perforated domain, real analytic continuation in Banach space, singularly perturbed domain, Mathematics (all), Engineering (all) |
| الوصف: | We consider a periodically perforated domain obtained by making in $\mathbb{R}^n$ a periodic set of holes, each of them of size proportional to $\epsilon$. Then we introduce a nonlinear boundary value problem for the Lam\'e equations in such a periodically perforated domain. The unknown of the problem is a vector valued function $u$ which represents the displacement attained in the equilibrium configuration by the points of a periodic linearly elastic matrix with a hole of size $\epsilon$ contained in each periodic cell. We assume that the traction exerted by the matrix on the boundary of each hole depends (nonlinearly) on the displacement attained by the points of the boundary of the hole. Then our aim is to describe what happens to the displacement vector function $u$ when $\epsilon$ tends to $0$. Under suitable assumptions we prove the existence of a family of solutions $\{u(\epsilon,\cdot)\}_{\epsilon\in]0,\epsilon'[}$ with a prescribed limiting behaviour when $\epsilon$ approaches $0$. Moreover, the family $\{u(\epsilon,\cdot)\}_{\epsilon\in]0,\epsilon'[}$ is in a sense locally unique and can be continued real analytically for negative values of $\epsilon$. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | STAMPA |
| اللغة: | English |
| العلاقة: | info:eu-repo/semantics/altIdentifier/wos/WOS:000328015100009; volume:37; issue:1; firstpage:106; lastpage:122; numberofpages:17; journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES; http://hdl.handle.net/11577/3281320Test; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-84890552427 |
| DOI: | 10.1002/mma.2788 |
| الإتاحة: | https://doi.org/10.1002/mma.2788Test http://hdl.handle.net/11577/3281320Test |
| رقم الانضمام: | edsbas.F667E8CB |
| قاعدة البيانات: | BASE |
| DOI: | 10.1002/mma.2788 |
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