Boundary stabilization of elastodynamic systems. Part I: Rellich-type relations for a problem in elasticity involving singularities.

Romain Brossard (1) , Jean-Pierre Lohéac (1)

1 ICJ - Institut Camille Jordan

For the Lamé's system, mixed boundary conditions generate singularities in the solution, mainly when the boundary of the domain is connected. We here prove Rellich relations involving these singularities. These relations are useful in the problem of boundary stabilization of the elastodynamic system when using the multipliers method. This problem is studied in Part II.

Mots clés: P.D.E

Mots clés: P.D.E.; Mixed boundary conditions; Singularities; Lamé system

Domaines: Equations aux dérivées partielles [math.AP]

Romain Brossard, Jean-Pierre Lohéac. Boundary stabilization of elastodynamic systems. Part I: Rellich-type relations for a problem in elasticity involving singularities.. 2007. ⟨hal-00196913v3⟩