A local uniqueness result for a quasi-linear heat transmission problem in a periodic two-phase dilute composite

Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (SciVal)

Abstract

We consider a quasi-linear 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, 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. For small enough the problem is known to have a solution, i.e., a pair of functions which determine the temperature distribution in the two materials. Then we prove a limiting property and a local uniqueness result for families of solutions which converge as tends to 0.

Original languageEnglish
Title of host publicationRecent Trends in Operator Theory and Partial Differential Equations
EditorsVladimir Maz'ya , David Natroshvili, Eugene Shargorodsky
PublisherSpringer Nature
Pages193-227
Number of pages35
Volume258
ISBN (Electronic)978-3-319-47079-5
ISBN (Print)978-3-319-47077-1, 3319470779
DOIs
Publication statusPublished - 15 Mar 2017

Publication series

NameOperator Theory: Advances and Applications
Volume258

Keywords

  • Asymptotic behavior
  • Existence
  • Local uniqueness
  • Periodic two-phase dilute composite
  • Quasi-linear heat transmission problem
  • Singularly perturbed domain

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