Semi-Linear Elliptic Problems in Composite Domains with Contact Resistance

par Faker Ben Belgacem (UTC)

mardi 23 sept. 2025, 14:00 → 15:00 Europe/Paris

UTC - GI

We focus on the mathematical analysis of the steady-state heat conduction problem in a multi-layered domain, with a non-linear Kapitza contact resistance at the interface, which slows down heat transfer. A maximum principle is first established, followed by a proof of existence by  applying the Schauder fixed point theorem to the variational formulation. Non-uniqueness is then illustrated through a simple one-dimensional example of a two layered-domain. Solutions are computed as fixed points of certain algebraic mappings, using Picard's iterative method. A co-dimension-one bifurcation analysis of these maps is then presented, with the ratio of the conductivities of the two layers  used as the control parameter. Two classes of (power-law) Kapitza conductance give rise to different types of bifurcations, including transcritical, supercritical, flip, and saddle-node bifurcations.