Skip to main content
Log in

Asymptotic behaviour for electromagnetic fields in the ionosphere

  • Published:
Annali dell’Università di Ferrara Aims and scope Submit manuscript

Sunto

In questo lavoro si studia la teoria lineare dell’elettromagnetismo nella ionosfera, caratterizzata da un’equazione costitutiva che associa la presenza di effetti di memoria all’azione attuale del campo elettrico. Dopo aver trattato le restrizioni termodinamiche all’equazione costitutiva prescelta, si dimostra l’esistenza di un dominio di dipendenza. Infine, si determina il comportamento asintotico delle soluzioni, nonché esistenza ed unicità delle stesse.

Abstract

We consider the linear theory of the Electromagnetism in the ionosphere characterized by a constitutive equation which associates the presence of memory effects with the actual action of the electric field. After studying the thermodynamic restrictions on the assumed constitutive equations, a domain of dependence inequality is derived. Then, asymptotic behaviour of solutions is studied together with uniqueness and existence theorems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. G. Gentili,Thermodynamic potentials for electromagnetic fields in the ionosphere, Int. J Engng. Sci.,11 (33) (1995), pp. 1561–1575.

    Article  MathSciNet  Google Scholar 

  2. M. Marziani,The ereditary theoretical approach to nonlinear phenomena in the ionosphere, Acc. Sc. Fe.,66 (1989), pp. 211.

    Google Scholar 

  3. D. Graffi,Una teoria ereditaria dell’effetto Lussemburgo, Rend. Sem. Mat. Univ. Padova,7 (1956), pp. 36–54.

    Google Scholar 

  4. A. V. Gurevich,Non-linear phenomena in the ionosphere, Springer, Berlin, 1994.

    Google Scholar 

  5. B. D. ColemanE. H. Dill,On the Thermodynamics of electromagnetic fields in materials with memory, Arch. Rational Mech. Anal.,41 (1971), pp. 132–162.

    Article  MathSciNet  Google Scholar 

  6. B. D. ColemanE. H. Dill,Thermodynamic restrictions on the constitutive equations of electromagnetic theory, ZAMP,22 (1971), pp. 691–702.

    Article  MATH  Google Scholar 

  7. W. Noll,A new mathematical theory of simple materials, Arch. Rational Mech. Anal.,48 (1972), pp. 1–50.

    Article  MATH  MathSciNet  Google Scholar 

  8. B. D. ColemanD. R. Owen,A mathematical foundation of Thermodynamics, Arch. Rational Mech. Anal.,54 (1974), pp. 1–104.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. FabrizioG. GentiliD. W. Reynolds,On rigid linear heat conductors with memory, Int. J. Engng. Sci.,36 (1998), pp. 765–782.

    Article  MathSciNet  Google Scholar 

  10. M. FabrizioC. GiorgiA. Morro,Free energies and dissipation properties for systems with memory, Arch. Rational Mech. Anal.,125 (1994), pp. 341–373.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. FabrizioB. LazzariJ. E. M. Rivera,Asymptotic behaviour in linear thermoelasticity, J. Math. Anal. Appl.,232 (1999), pp. 138–165.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. FabrizioA. Morro,Mathematical problems in linear viscoelasticity, SIAM Studies in Applied Mathematics, Phyladelphia, 1992.

    MATH  Google Scholar 

  13. C. A. BoselloR. Nibbi,A principle of constrained minimum in electromagnetism, Int. J. Engng. Sci.,37 (1998), pp. 253–268.

    Article  MathSciNet  Google Scholar 

  14. G. Amendola,Asymptotic behaviour in a conducting electromagnetic medium, IMA J. Appl. Math.,64 (2000), pp. 271–282.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Amendola,Linear stability for a thermoelectromagnetic material with memory, Quart. Appl. Math., LIX,1 (2001), pp. 67–84.

    MathSciNet  Google Scholar 

  16. C. H. Wilcox,The steady-state diffraction of electromagnetic radiation by an obstacle in an inhomogeneous anisotropic conducting medium, Arch. Rational Mech. Anal.,14 (1963), pp. 326–336.

    Article  MATH  MathSciNet  Google Scholar 

  17. C. H. Wilcox,The domain of dependence inequality for symmetric hyperbolic systems, Boll. Am. Math. Soc.,70 (1964), pp. 149–154.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amendola, G. Asymptotic behaviour for electromagnetic fields in the ionosphere. Ann. Univ. Ferrara 48, 165–187 (2002). https://doi.org/10.1007/BF02824745

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02824745

Keywords

Navigation