Observability  of $N$-dimensional integro-differential systems

Paola Loreti; Daniela  Sforza

doi:10.3934/dcdss.2016026

Article Contents

2016, Volume 9, Issue 3: 745-757. Doi: 10.3934/dcdss.2016026

This issue Previous Article Inverse problems for evolution equations with time dependent operator-coefficients Next Article Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions

Observability of $N$-dimensional integro-differential systems

Paola Loreti^1, and
Daniela Sforza^2,

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma
2.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Via Antonio Scarpa 16 I-00161 Roma

Received: February 28, 2015

Revised: August 31, 2015

Published: May 2016

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Abstract

The aim of the paper is to show a reachability result for the solution of a multidimensional coupled Petrovsky and wave system when a non local term, expressed as a convolution integral, is active. Motivations to the study are in linear acoustic theory in three dimensions. To achieve that, we prove observability estimates by means of Ingham type inequalities applied to the Fourier series expansion of the solution.

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Mathematics Subject Classification: Primary: 93B05, 45K05; Secondary: 42A38.

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