Steady conduction problems with non-linear Kapitza contact resistance: Existence and non-uniqueness

E. Bejaoui, F. Ben Belgacem, F. Jelassi and J. Ma

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 311-324

Abstract: We focus on the steady-state heat conduction problem in a two-layer domain, with a non-linear contact resistance at the interface. This Kapitza resistance is known to slow down heat transfer and leads to a temperature jump. A maximum principle is first established. Then, we prove an existence result by applying the Schauder fixed point theorem to the variational formulation. To address the non-uniqueness, we consider a one-dimensional model. Solutions are computed as fixed points of specific algebraic mappings using Picard’s iterative method. We present a co-dimension-one bifurcation analysis of these maps, with the ratio of the two layers’ conductivities considered as the control parameter. Two classes of (power-law) Kapitza conductance lead to different types of bifurcations, including transcritical, supercritical, flip, and saddle–node.

Keywords: Thermal contact resistance; Semi-linear elliptic problem; Maximum principle; Schauder fixed point theorem; Bifurcation of maps (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:311-324

DOI: 10.1016/j.matcom.2026.04.010

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