Long-time dynamics of N-dimensional structure equations with thermal memory
| Autor: | Jianwen Zhang, Danxia Wang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
Thermal source N dimensional thermal memory 010102 general mathematics Mathematical analysis Structure (category theory) lcsh:QA299.6-433 global attractor lcsh:Analysis 01 natural sciences Omega thermoelastic coupled structure Past history 010101 applied mathematics internal (structural) damping Time dynamics Thermal Nabla symbol 0101 mathematics asymptotically smooth Analysis Mathematics |
| Zdroj: | Boundary Value Problems, Vol 2017, Iss 1, Pp 1-21 (2017) |
| ISSN: | 1687-2770 |
| DOI: | 10.1186/s13661-017-0864-z |
| Popis: | This paper is concerned with the long-time behavior for a class of N-dimensional thermoelastic coupled structure equations with structural damping and past history thermal memory $$\begin{gathered} u_{tt}+\triangle^{2}u+\nu \triangle\theta+\triangle^{2}u_{t}-\biggl[\sigma \biggl( \int_{\Omega}(\nabla u)^{2}\,dx\biggr)+\phi\biggl( \int_{\Omega}\nabla u\nabla u_{t}\,dx\biggr)\biggr] \triangle u+f_{1}(u) \\ \quad=q_{1}(x),\quad \mbox{in }\Omega\times R^{+}, \\ \theta_{t}-\iota\triangle\theta-(1-\iota) \int_{0}^{\infty }k(s)\triangle\theta(t-s)\,ds-\nu \triangle u_{t}+f_{2}(\theta )=q_{2}(x),\quad \mbox{with } 0\leq\iota< 1. \end{gathered} $$ This system arises from a model of the nonlinear thermoelastic coupled vibration structure with the clamped ends for simultaneously considering the medium damping, the viscous effect and the nonlinear constitutive relation and thermoelasticity based on a theory of non-Fourier heat flux laws. By considering the case where the internal (structural) damping is present, for $0\leq\iota |
| Databáze: | OpenAIRE |
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