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Asymptotic stability in thermoelectromagnetism with memory
Author(s) -
Lazzari Barbara,
Nibbi Roberta
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19991110)22:16<1375::aid-mma81>3.0.co;2-i
Subject(s) - exponential stability , mathematics , thermal conduction , domain (mathematical analysis) , homogeneous , heat equation , stability (learning theory) , mathematical analysis , thermodynamics , physics , nonlinear system , quantum mechanics , combinatorics , machine learning , computer science
A model describing a linear homogeneous dielectric with memory which obeys the Cattaneo–Maxwell law for the heat conduction is presented. The restrictions on the constitutive functionals are found as a direct consequence of the Second Law of Thermodynamics and some free energy potentials exhibited. Such potentials allow to determine a domain of dependence theorem for the first‐order integro‐differential system of equations governing the evolution of the thermoelectromagnetic radiation. The dissipativity due to the memory and to the heat conduction allows to establish some estimates on the asymptotic behaviour and prove the exponential decay of the solution of the system in absence of external sources. Copyright © 1999 John Wiley & Sons, Ltd.