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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce a Matlab program method to compute Carlemanestimate for the fourth order partial differential operator$\gamma\partial_t+\partial_x^4\ (\gamma\in\mathbb{R})$. We obtain two kinds ofCarleman estimates with different weight functions, i.e. singular weightfunction and regular weight function, respectively. Based on Carleman estimatewith singular weight function, one can obtain the known controllability andobservability results for the 1-d fourth order parabolic-type equation, whilebased on Carleman estimate with regular weight function, one can deduce notonly the known result on conditional stability in the inverse problem ofhalf-order fractional diffusion equation, but also a new result on conditionalstability in the inverse problem of half-order fractional Schr\"odingerequation.

Matlab program method of computing Carleman estimates and applications