Control and exponential stability for a transmission problem of a viscoelastic wave equation

Rémi Buffe (1, 2) , Marcelo M. Cavalcanti (3) , Valéria N. Domingos Cavalcanti (3) , Ludovick Gagnon (1, 2)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 UEM - Universidade Estadual de Maringá [Brasil] = State University of Maringá [Brazil] = Université d'État de Maringá [Brésil]

In this article, we consider the energy decay of a viscoelastic wave in an heterogeneous medium. To be more specific, the medium is composed of two different homogeneous medium with a memory term located in one of the medium. We prove exponential decay of the energy of the solution under geometrical and analytical hypothesis on the memory term.

Mots clés: viscoelastic effect; exponential stability; wave equation; transmission problem

Domaines: Equations aux dérivées partielles [math.AP]

Rémi Buffe, Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Ludovick Gagnon. Control and exponential stability for a transmission problem of a viscoelastic wave equation. 2020. ⟨hal-02473477⟩