A singularly perturbed nonlinear traction problem in a periodically perforated domain. A functional analytic approach
| Autor: | Matteo Dalla Riva, Paolo Musolino |
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| Rok vydání: | 2013 |
| Předmět: |
integral operators
nonlinear boundary value problems for linear elliptic equations General Mathematics Traction (engineering) integral representations integral equation methods linearized elastostatics periodically perforated domain real analytic continuation in Banach space singularly perturbed domain Mathematics (all) Engineering (all) Boundary (topology) 01 natural sciences Domain (mathematical analysis) Displacement (vector) Matrix (mathematics) Mathematics - Analysis of PDEs Settore MAT/05 - Analisi Matematica FOS: Mathematics 0101 mathematics 35J65 31B10 45F15 74B05 Physics 010102 general mathematics Mathematical analysis General Engineering integral representations integral operators integral equation methods Function (mathematics) 010101 applied mathematics Nonlinear system Vector-valued function Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1306.6177 |
| Popis: | We consider a periodically perforated domain obtained by making in 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,.) : \epsilon \in ]0,\epsilon'[} with a prescribed limiting behaviour when \epsilon approaches 0. Moreover, the family {u(\epsilon,.) : \epsilon \in ]0,\epsilon'[} is in a sense locally unique and can be continued real analytically for negative values of \epsilon. |
| Databáze: | OpenAIRE |
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