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- W4308164923 abstract "The main objective of this paper is to establish the null controllability for the fourth order semilinear parabolic equations with the nonlinearities involving the state and its gradient up to second order. First of all, based on optimal control theory of partial differential equations and global Carleman estimates 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 term and some linear terms including the derivatives of the state up to second order. Then we prove the null controllability of the fourth order semilinear parabolic equations by such global Carleman estimates and the Leray-Schauder's fixed points theorem." @default.
- W4308164923 created "2022-11-08" @default.
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- W4308164923 date "2022-11-01" @default.
- W4308164923 modified "2023-09-29" @default.
- W4308164923 title "Global Carleman estimates for the fourth order parabolic equations and application to null controllability" @default.
- W4308164923 doi "https://doi.org/10.48550/arxiv.2211.00647" @default.
- W4308164923 hasPublicationYear "2022" @default.
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