English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the linear system of viscoelasticity with the homogeneousDirichlet boundary condition. First we prove a Carleman estimate with boundaryvalues of solutions of viscoelasticity system. Since a solution $u$ underconsideration is not assumed to have compact support, in the decoupling of theLam\'e operator by introducing div $u$ and rot $u$, we have no boundarycondition for them, so that we have to carry out arguments by apseudodifferential operator. Second we apply the Carleman estimate to aninverse source problem of determining a spatially varying factor of theexternal source in the linear viscoelastitiy by extra Neumann data on thelateral subboundary over a sufficiently long time interval and establish thestability estimate.

Carleman estimate for linear viscoelasticity equations and an inverse source problem