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

Heidari, Hanif; Malek, Alaeddin

Int. J. Appl. Math. 22, No. 4, 615-626 (2009).

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

Keywords:

hyperdiffusion equation; controllability; moment problem; biorthogonal sequence