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- W2952389441 abstract "Let $OmsubsetRR^N$ a bounded domain with a Lipschitz continuous boundary. We study the controllability of the space-time fractional diffusion equation begin{equation*} begin{cases} mathbb D_t^alpha u+(-Delta)^su=0;;&mbox{ in };(0,T)timesOmega u=g &mbox{ in };(0,T)times(RR^NsetminusOmega) u(0,cdot)=u_0&mbox{ in };Omega, end{cases} end{equation*} where $u=u(t,x)$ is the state to be controlled and $g=g(t,x)$ is the control function which is localized in a subset $mathcal O$ of $Omc$. Here, $0 0$ be real numbers. After giving an explicit representation of solutions, we show that the system is always approximately controllable for every $T>0$, $u_0in L^2(Omega)$ and $gin mathcal D((0,T)timesmathcal O)$ where $mathcal Osubset(RR^NsetminusbOm)$ is any open set. The results obtained are sharp in the sense that such a system is never null controllable if $0<alpha<1$. The proof of our result is based on a new unique continuation principle for the eigenvalues problem associated with the fractional Laplace operator subject to the zero exterior boundary condition that we have established." @default.
- W2952389441 created "2019-06-27" @default.
- W2952389441 creator A5026604673 @default.
- W2952389441 date "2018-02-22" @default.
- W2952389441 modified "2023-09-23" @default.
- W2952389441 title "Approximate controllabilty from the exterior of space-time fractional diffusive equations" @default.
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