Dissipativity and irreversibility of electromagnetic systems

Mathematical Models and Methods in Applied Sciences

Volumn 10, Issue 2, 2000, Pages 217-246

  Fabrizio, Mauro ^a   Morro, Angelo ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034413949     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202500000148     Document Type: Article

References (22)

1. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984), §77-80.
2. J. D. Jackson, Classical Electrodynamics (Wiley, 1975), Chap. 7.
3. V. Volterra, Theory of Functionals (Blackie, 1930).
4. D. Graffi, Sui problemi della ereditarietà lineare, Nuovo Cimento 5 (1928) 53-71.
5. B. D. Coleman and E. H. Dill, Thermodynamic restrictions on the constitutive equations of electromagnetic theory, Z. Angew. Math. Phys. 22 (1971) 691-702.
6. B. D. Coleman and E. H. Dill, On the thermodynamics of electromagnetic fields in materials with memory, Arch. Rational Mech. Anal. 41 (1971) 132-162.
7. A. C. Eringen and G. A. Maugin, Electrodynamics of Continua I (Academic Press, 1990), Chap. 13.
8. M. E. Gurtin, Dynamical theories of electromagnetism and superconductivity based on gauge invariance and energy, Arch. Rational Mech. Anal. 137 (1997) 1-25.
9. W. Noll, A new mathematical theory of simple materials, Arch. Rational Mech. Anal. 48 (1972) 1-50.
10. B. D. Coleman and D. R. Owen, A mathematical foundation for thermodynamics, Arch. Rational Mech. Anal. 64 (1974) 1-104.
11. B. D. Coleman and D. R. Owen, On the thermodynamics of semi-systems with restrictions on the accessibility of states, Arch. Rational Mech. Anal. 66 (1977) 173-182.
12. A. Visintin, Differential Models of Hysteresis (Springer, 1994).
13. A. V. Gurevich, Nonlinear Phenomena in the Ionosphere (Springer, 1978).
14. M. Marziani, The hereditary theoretical approach to nonlinear phenomena in the ionosphere, Acc. Sci. Ferrara 66 (1988-1990) 211-225.
15. D. Graffi, Una teoria ereditaria dell'effetto Lussemburgo, Rend. Sem. Mat. Univ. Padova 7 (1956) 36-54.
16. M. Fabrizio and A. Morro, Reversible processes in the thermodynamics of continuous media, J. Nonequilib. Thermodyn. 16 (1991) 1-12.
17. M. Fabrizio, C. Giorgi and A. Morro, Free energies and dissipation properties for systems with memory, Arch. Rational Mech. Anal. 125 (1994) 341-373.
18. M. Fabrizio and A. Morro, Mathematical Problems in Linear Viscoelasticity (SIAM, 1992), Chap. 3.
19. G. Gentili, Free enthalpies, free energies and norms for dielectrics with fading memory, Cont. Mech. Thermodyn. (1996) 201-214.
20. M. Fabrizio, C. Giorgi and A. Morro, Internal dissipation, relaxation property, and free energy in materials with fading memory, J. Elasticity 40 (1995) 107-122.
21. G. Gentili, Thermodynamic potentials for electromagnetic fields in the ionosphere, Internat. J. Engrg. Sci. 33 (1995) 1561-1575.
22. M. Fabrizio and A. Morro, A boundary condition with memory in electromagnetism, Arch. Rational Mech. Anal. 136 (1997) 359-381.