The equation studied in this paper, proposed by Gurtin and Pipkin, is used to describe thermal processes with memory, or non-Fickian diffusion (as is the case in presence of complex molecular structures). In this paper we prove that control problems for the Gurtin-Pipkin equation can be reduced to a moment problem and it turns out that existing controllability results (also derived by the author) imply that the sequence of functions used to describe the moment problem is a Riesz sequence. Furthermore, we study the biorthogonal of this Riesz sequence in order to give a constructive method for the computation of the control steering a given initial condition to a prescribed target.
Riesz Systems and Controllability of Heat Equations with Memory / PANDOLFI L.. - In: INTEGRAL EQUATIONS AND OPERATOR THEORY. - ISSN 0378-620X. - 64(2009), pp. 429-453. [10.1007/s00020-009-1682-1]
|Titolo:||Riesz Systems and Controllability of Heat Equations with Memory|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00020-009-1682-1|
|Appare nelle tipologie:||1.1 Articolo in rivista|