On uniqueness and continuous dependence in nonlinear thermodynamics of electromagnetic materials
Author:
D. Ieşan
Journal:
Quart. Appl. Math. 48 (1990), 85-94
MSC:
Primary 73B30; Secondary 78A25, 80A20
DOI:
https://doi.org/10.1090/qam/1040235
MathSciNet review:
MR1040235
Full-text PDF Free Access
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Abstract: The paper is concerned with the boundary-initial-value problems of the nonlinear thermodynamics of electromagnetic materials. Uniqueness and continuous dependence results are established.
G. Pettini, Sul teorema di unicità nell’elettromagnetismo nonlineare ereditario, Boll. Un. Mat. Ital., 55–64 (1974)
- Mauro Fabrizio, Problemi di unicità per le equazioni funzionali non lineari del campo elettromagnetico. I, II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 49 (1970), 200–207 (1971); ibid. (8) 49 (1970), 268–271 (1971) (Italian, with English summary). MR 314365
- Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980. MR 580946
- C. M. Dafermos, The second law of thermodynamics and stability, Arch. Rational Mech. Anal. 70 (1979), no. 2, 167–179. MR 546634, DOI https://doi.org/10.1007/BF00250353
- S. Chiriţă, Uniqueness and continuous data dependence in dynamical problems of nonlinear thermoelasticity, J. Thermal Stresses 5 (1982), no. 3-4, 331–346. MR 695432, DOI https://doi.org/10.1080/01495738208942154
B. D. Coleman and E. H. Dill, Thermodynamical restrictions on the constitutive equations of electromagnetic theory, Z. Angew. Math. Phys. 22, 691–702 (1971)
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- Mauro Fabrizio, Théorèmes d’unicité sur un nouveau problème aux limites relatif aux équations non linéaires de Maxwell, J. Mécanique 15 (1976), no. 4, 681–696. MR 434159
G. Pettini, Sul teorema di unicità nell’elettromagnetismo nonlineare ereditario, Boll. Un. Mat. Ital., 55–64 (1974)
M. Fabrizio, Problemi di unicità per le equazioni funzionali non lineari del campo elettromagnetico I, II, Rend. Acc. Naz. Lincei 49, I:200–207, II:268–271 (1970)
D. Graffi, Nonlinear Partial Differential Equations in Physical Problems, Pitman, Boston-London-Melbourne, 1980
C. M. Dafermos, The second law of thermodynamics and stability, Arch. Rational Mech. Anal. 70, 167–179 (1979)
S. Chiriţǎ, Uniqueness and continuous data dependence in dynamical problems of nonlinear thermoelasticity, J. Thermal Stresses 5, 331–346 (1982)
B. D. Coleman and E. H. Dill, Thermodynamical restrictions on the constitutive equations of electromagnetic theory, Z. Angew. Math. Phys. 22, 691–702 (1971)
B. D. Coleman and E. H. Dill, On the thermodynamics of electromagnetic fields in materials with memory, Arch. Rational Mech. Anal. 41, 132–162 (1971)
M. F. McCarthy, Thermodynamics of electromagnetic materials with memory, Arch. Rational Mech. Anal. 41, 333–353 (1971)
M. Fabrizio, Sulla convessità dei potenziali termodinamici per materiali con memoria, Ann. Mat. Pura Appl. 101, 33–48 (1974)
M. Fabrizio, Théorémes d’unicité sur un nouveau problème au limites relatif aux équations non linéaires de Maxwell, J. Mécanique 15, 681–695 (1976)
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Article copyright:
© Copyright 1990
American Mathematical Society
