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 ϵ, 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 ϵ 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 ϵ tends to 0.
Dedicated to Professor Roland Duduchava on the occasion of his 70th anniversary
Mathematics Subject Classification (2010). Primary 35J25; Secondary 31B10, 45F15, 47H30.
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Riva, M.D., de Cristoforis, M.L., Musolino, P. (2017). A Local Uniqueness Result for a Quasi-linear Heat Transmission Problem in a Periodic Two-phase Dilute Composite. In: Maz'ya, V., Natroshvili, D., Shargorodsky, E., Wendland, W. (eds) Recent Trends in Operator Theory and Partial Differential Equations. Operator Theory: Advances and Applications, vol 258. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47079-5_10
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DOI: https://doi.org/10.1007/978-3-319-47079-5_10
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-47077-1
Online ISBN: 978-3-319-47079-5
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