## Null boundary controllability for hyperdiffusion equation.(English)Zbl 1177.93018

In this paper we establish null boundary controllability of the hyperdiffusion equation. The problem of null boundary controllability is reduced to a moment problem. The moment problem is solved by using a biorthogonal sequence with respect to real exponential bases. Existence and uniqueness of the specific biorthogonal sequence are proved and it is shown that the biorthogonal sequence has corresponding minimal $$L^2(0,T)$$ norm.

### MSC:

 93B05 Controllability 93C20 Control/observation systems governed by partial differential equations 35K35 Initial-boundary value problems for higher-order parabolic equations 92B05 General biology and biomathematics