论文标题
全球Carleman估计第四阶抛物线方程和对无可控性的应用
Global Carleman estimates for the fourth order parabolic equations and application to null controllability
论文作者
论文摘要
本文的主要目的是建立第四阶半线性抛物线方程的无效可控性，其非线性涉及国家及其梯度到二阶。 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.然后，我们通过此类全球Carleman估计值和Leray-Schauder的固定点定理证明了第四阶半线性抛物线方程的无效可控性。
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.
