Linking hyperbolic and parabolic p.d.e.'s.

Hans Zwart (1) , Yann Le Gorrec (2) , Bernhard Maschke (3)

1 Department of Appliled Mathematics. - Department of Appliled Mathematics.
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
3 LAGEP - Laboratoire d'automatique et de génie des procédés

In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.'s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain existence and uniqueness of solutions for the uniform elliptic p.d.e.'s and for the Schr¨odinger equation.

Domaines: Micro et nanotechnologies/Microélectronique

Hans Zwart, Yann Le Gorrec, Bernhard Maschke. Linking hyperbolic and parabolic p.d.e.'s.. 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'11., Dec 2011, Orlando, Floride, United States. pp.4921-4924. ⟨hal-00720347⟩