Determining a boundary coefficient in a dissipative wave equation: uniqueness and directional Lipschitz stability

Abstract : We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that uniqueness holds at the origin provided that the initial condition is appropriately chosen. We show that the choice of the initial condition leading to uniqueness is related to a fine version of the unique continuation property for elliptic operators. We also establish a Lipschitz directional stability estimate at the origin, which is obtained by a linearization process.
Document type :
Journal articles
Complete list of metadatas

https://hal.uvsq.fr/hal-02184498
Contributor : Équipe Hal Uvsq <>
Submitted on : Tuesday, July 16, 2019 - 10:15:24 AM
Last modification on : Thursday, July 18, 2019 - 2:52:06 PM

Links full text

Identifiers

Citation

Kaïs Ammari, Mourad Choulli. Determining a boundary coefficient in a dissipative wave equation: uniqueness and directional Lipschitz stability. Semigroup Forum, Springer Verlag, 2016, 95 (3), pp.527-538. ⟨10.1007/s00233-016-9845-2⟩. ⟨hal-02184498⟩

Share

Metrics

Record views

20