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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The approach to Lipschitz stability for uniformly parabolic equationsintroduced by Imanuvilov and Yamamoto in 1998, based on Carleman estimates,seems hard to apply to the case of Grushin-type operators of interest to thispaper. Indeed, such estimates are still missing for parabolic operatorsdegenerating in the interior of the space domain. Nevertheless, we are able toprove Lipschitz stability results for inverse source problems for suchoperators, with locally distributed measurements in arbitrary space dimension.For this purpose, we follow a mixed strategy which combines the appraoch due toLebeau and Robbiano, relying on Fourier decomposition, with Carlemaninequalities for heat equations with nonsmooth coefficients (solved by theFourier modes). As a corollary, we obtain a direct proof of the observabilityof multidimensional Grushin-type parabolic equations, with locally distributedobservations, which is equivalent to null controllability with locallydistributed controls.

Inverse source problem and null controllability for multidimensional parabolic operators of Grushin type