A quasi-linear heat transmission problem in a periodic two-phase dilute composite. A functional analytic approach
| Autor: | aolo Musolino, Massimo Lanza de Cristoforis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Physics
Asymptotic analysis Euclidean space Applied Mathematics Mathematical analysis Structure (category theory) Phase (waves) Thermodynamics Distribution (mathematics) Settore MAT/05 - Analisi Matematica Thermal Quasi-linear heat transmission problem singularly perturbed domain periodic two-phase dilute composite asymptotic behavior real analytic continuation in Banach space Series expansion Analysis Convergent series |
| Popis: | We consider a heat transmission problem for a composite material which fills the $n$-dimensional Euclidean space. The composite has a periodic structure and consists of two materials. In each periodicity cell one material occupies a cavity of size $\epsilon$, and the second material fills the remaining part of the cell. We assume that the thermal conductivities of the materials depend nonlinearly upon the temperature. We show that for $\epsilon$ small enough the problem has a solution, \textit{i.e.}, a pair of functions which determine the temperature distribution in the two materials. Then we analyze the behavior of such a solution as $\epsilon$ approaches $0$ by an approach which is alternative to those of asymptotic analysis. In particular we prove that if $n\geq 3$, the temperature can be expanded into a convergent series expansion of powers of $\epsilon$ and that if $n=2$ the temperature can be expanded into a convergent double series expansion of powers of $\epsilon$ and $\epsilon \log \epsilon$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|