Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section

Sébastien Imperiale (1) , Patrick Joly (2)

1 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

This paper is the first contribution towards the rigorous justification of asymptotic 1D models for the time-domain simulation of the propagation of electromagnetic waves in coaxial cables. Our general objective is to derive error estimates between the "exact" solution of the full 3D model and the "approximate" solution of the 1D model known as the Telegraphist's equation.

Mots clés: Coaxial cables; Telegraphist's equation; Error estimates; Non-homogeneous cross-section

Domaines: Equations aux dérivées partielles [math.AP]

Sébastien Imperiale, Patrick Joly. Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section. Advances in Applied Mechanics, 2012, xx, ⟨10.4208/aamm.12-12S06⟩. ⟨hal-00875808v2⟩