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Some identities on weighted Sobolev spaces
An existence theorem for the magneto-viscoelastic problem
1. | Dipartimento di Scienze di Base e Applicate per l’Ingegneria, sez. matematica – 16, Via A. Scarpa, SAPIENZA Università di Roma, Rome, 00161, Italy, Italy |
2. | Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, Rome, 00185, Italy |
References:
[1] |
W. F. Brown, "Magnetoelastic Interactions,", Springer Tracts in Natural Philosophy, 9 (1966). Google Scholar |
[2] |
S. Carillo, V. Valente and G. Vergara, Caffarelli, Existence and uniqueness in magneto-viscoelasticity,, Applicable Analysis, (2010). Google Scholar |
[3] |
M. Chipot and G. Vergara-Caffarelli, Viscoelasticity without initial conditions,, in, 190 (1989), 52.
|
[4] |
M. Chipot and G. Vergara Caffarelli, Some results in viscoelasticity theory via a simple perturbation argument,, Rend. Sem. Mat. Univ. Padova, 84 (1990), 223.
|
[5] |
M. Chipot, I. Shafrir, V. Valente and G. Vergara-Caffarelli, A nonlocal problem arising in the study of magneto-elastic interactions,, Boll. UMI (9), 1 (2008), 197.
|
[6] |
M. Chipot, I. Shafrir, V. Valente and G. Vergara-Caffarelli, On a hyperbolic-parabolic system arising in magnetoelasticity,, J. Math. Anal. Appl., 352 (2009), 120.
doi: 10.1016/j.jmaa.2008.04.013. |
[7] |
C. M. Dafermos, An abstract Volterra equation with applications to linear viscoelasticity,, J. Diff. Equations, 7 (1970), 554.
doi: 10.1016/0022-0396(70)90101-4. |
[8] |
C. M. Dafermos, Asymptotic stability in viscoelasticity,, Arch. Rat. Mech. Anal., 37 (1970), 297.
doi: 10.1007/BF00251609. |
[9] |
T. L. Gilbert, A Lagrangian formulation of the gyromagnetic equation of the magnetization field,, Phys. Rev., 100 (1955). Google Scholar |
[10] |
S. He, "Modélisation et Simulation Numérique de Matériaux Magnétostrictifs,", Ph.D thesis, (1999). Google Scholar |
[11] |
D. Kinderlehrer, Magnetoelastic interactions,, in, 25 (1996), 177.
|
[12] |
L. Landau and E. Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies,, Phys. Z. Sowjet., 8 (1935). Google Scholar |
[13] |
D. Sforza and G. Vergara-Caffarelli, A Volterra integro-differential equation "without initial conditions,", Adv. Math. Sci. Appl., 11 (2001), 153.
|
[14] |
V. Valente and G. Vergara-Caffarelli, On the dynamics of magneto-elastic interactions: Existence of solutions and limit behaviors,, Asymptotic Analysis, 51 (2007), 319.
|
[15] |
G. Vergara-Caffarelli, Dissipatività e unicità per il problema dinamico unidimensionale della viscoelasticità lineare,, Atti Accad. Naz. Lincei, 82 (1988), 483. Google Scholar |
[16] |
G. Vergara-Caffarelli, Dissipatività ed esistenza per il problema dinamico unidimensionale della viscoelasticità lineare,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 82 (1988), 489.
|
show all references
References:
[1] |
W. F. Brown, "Magnetoelastic Interactions,", Springer Tracts in Natural Philosophy, 9 (1966). Google Scholar |
[2] |
S. Carillo, V. Valente and G. Vergara, Caffarelli, Existence and uniqueness in magneto-viscoelasticity,, Applicable Analysis, (2010). Google Scholar |
[3] |
M. Chipot and G. Vergara-Caffarelli, Viscoelasticity without initial conditions,, in, 190 (1989), 52.
|
[4] |
M. Chipot and G. Vergara Caffarelli, Some results in viscoelasticity theory via a simple perturbation argument,, Rend. Sem. Mat. Univ. Padova, 84 (1990), 223.
|
[5] |
M. Chipot, I. Shafrir, V. Valente and G. Vergara-Caffarelli, A nonlocal problem arising in the study of magneto-elastic interactions,, Boll. UMI (9), 1 (2008), 197.
|
[6] |
M. Chipot, I. Shafrir, V. Valente and G. Vergara-Caffarelli, On a hyperbolic-parabolic system arising in magnetoelasticity,, J. Math. Anal. Appl., 352 (2009), 120.
doi: 10.1016/j.jmaa.2008.04.013. |
[7] |
C. M. Dafermos, An abstract Volterra equation with applications to linear viscoelasticity,, J. Diff. Equations, 7 (1970), 554.
doi: 10.1016/0022-0396(70)90101-4. |
[8] |
C. M. Dafermos, Asymptotic stability in viscoelasticity,, Arch. Rat. Mech. Anal., 37 (1970), 297.
doi: 10.1007/BF00251609. |
[9] |
T. L. Gilbert, A Lagrangian formulation of the gyromagnetic equation of the magnetization field,, Phys. Rev., 100 (1955). Google Scholar |
[10] |
S. He, "Modélisation et Simulation Numérique de Matériaux Magnétostrictifs,", Ph.D thesis, (1999). Google Scholar |
[11] |
D. Kinderlehrer, Magnetoelastic interactions,, in, 25 (1996), 177.
|
[12] |
L. Landau and E. Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies,, Phys. Z. Sowjet., 8 (1935). Google Scholar |
[13] |
D. Sforza and G. Vergara-Caffarelli, A Volterra integro-differential equation "without initial conditions,", Adv. Math. Sci. Appl., 11 (2001), 153.
|
[14] |
V. Valente and G. Vergara-Caffarelli, On the dynamics of magneto-elastic interactions: Existence of solutions and limit behaviors,, Asymptotic Analysis, 51 (2007), 319.
|
[15] |
G. Vergara-Caffarelli, Dissipatività e unicità per il problema dinamico unidimensionale della viscoelasticità lineare,, Atti Accad. Naz. Lincei, 82 (1988), 483. Google Scholar |
[16] |
G. Vergara-Caffarelli, Dissipatività ed esistenza per il problema dinamico unidimensionale della viscoelasticità lineare,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 82 (1988), 489.
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