Long-time dynamics of vectorial von Karman system with nonlinear thermal effects and free boundary conditions
| Autor: | Rodrigo Nunes Monteiro, Irena Lasiecka, To Fu Ma |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Dynamical systems theory Applied Mathematics MECÂNICA DOS SÓLIDOS 010102 general mathematics Mathematical analysis Scalar (physics) Shell (structure) Moment of inertia 01 natural sciences Physics::Fluid Dynamics 010101 applied mathematics Nonlinear system Flow (mathematics) Attractor Discrete Mathematics and Combinatorics Boundary value problem 0101 mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1553-524X |
| DOI: | 10.3934/dcdsb.2018141 |
| Popis: | This paper is concerned with long-time dynamics of a full von Karman system subject to nonlinear thermal coupling and free boundary conditions. In contrast with scalar von Karman system, vectorial full von Karman system accounts for both vertical and in plane displacements. The corresponding PDE is of critical interest in flow structure interactions where nonlinear plate/shell dynamics interacts with perturbed flows [vicid or invicid] [ 8 , 9 , 15 ]. In this paper it is shown that the system admits a global attractor which is also smooth and of finite fractal dimension. The above result is shown to hold for plates without regularizing effects of rotational inertia and without any mechanical dissipation imposed on vertical displacements. This is in contrast with the literature on this topic [ 15 ] and references therein. In order to handle highly supercritical nature of the von Karman nonlinearities, new results on "hidden" trace regularity generated by thermal effects are exploited. These lead to asymptotic compensated compactness of trajectories which then allows to use newly developed tools pertaining to quasi stable dynamical systems [ 8 ]. |
| Databáze: | OpenAIRE |
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