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, Luciano. - In: INTEGRAL EQUATIONS AND OPERATOR THEORY. - ISSN 0378-620X. - 64:(2009), pp. 429-453. [10.1007/s00020-009-1682-1]
Riesz Systems and Controllability of Heat Equations with Memory
PANDOLFI, LUCIANO
2009
Abstract
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.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2279199
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