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

The main objective of this paper is to establish the null controllability forthe fourth order semilinear parabolic equations with the nonlinearitiesinvolving the state and its gradient up to second order. First of all, based onoptimal control theory of partial differential equations and global Carlemanestimates obtained in \cite{gs} for fourth order parabolic equation with$L^2(Q)$-external force, we establish the global Carleman estimates for the$L^2(Q)$ weak solutions of the same system with a low regularity external termand some linear terms including the derivatives of the state up to secondorder. Then we prove the null controllability of the fourth order semilinearparabolic equations by such global Carleman estimates and the Leray-Schauder'sfixed points theorem.

Global Carleman estimates for the fourth order parabolic equations and application to null controllability