Some expressions for the free energy in the case of incompressible viscoelastic fluids are given. These are derived from free energies already intro- duced for other viscoelastic materials, adapted to incompressible fluids. A new free energy is given in terms of the minimal state descriptor. The internal dis- sipations related to these different functionals are also derived. Two equivalent expressions for the minimum free energy are given, one in terms of the history of strain and the other in terms of the minimal state variable. This latter quan- tity is also used to prove a theorem of existence and uniqueness of solutions of initial boundary value problems for incompressible fluids. Finally, the evo- lution of the system is described in terms of a strongly continuous semigroup of linear contraction operators on a suitable Hilbert space. Thus, a theorem of existence and uniqueness of solutions admitted by such an evolution problem is proved. Also, exponential decay of the associated e

Some expressions for the free energy in the case of incompressible viscoelastic fluids are given. These are derived from free energies already introduced for other viscoelastic materials, adapted to incompressible fluids. A new free energy is given in terms of the minimal state descriptor. The internal dissipations related to these different functionals are also derived. Two equivalent expressions for the minimum free energy are given, one in terms of the history of strain and the other in terms of the minimal state variable. This latter quantity is also used to prove a theorem of existence and uniqueness of solutions to initial boundary value problems for incompressible fluids. Finally, the evolution of the system is described in terms of a strongly continuous semigroup of linear contraction operators on a suitable Hilbert space. Thus, a theorem of existence and uniqueness of solutions admitted by such an evolution problem is proved.

VISCOELASTIC FLUIDS: FREE ENERGIES, DIFFERENTIAL PROBLEMS AND ASYMPTOTIC BEHAVIOUR / Giovambattista, Amendola; Carillo, Sandra; John, Golden; Adele, Manes. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 19:7(2014), pp. 1815-1835. [10.3934/dcdsb.2014.19.1815]

VISCOELASTIC FLUIDS: FREE ENERGIES, DIFFERENTIAL PROBLEMS AND ASYMPTOTIC BEHAVIOUR

CARILLO, Sandra;
2014

Abstract

Some expressions for the free energy in the case of incompressible viscoelastic fluids are given. These are derived from free energies already intro- duced for other viscoelastic materials, adapted to incompressible fluids. A new free energy is given in terms of the minimal state descriptor. The internal dis- sipations related to these different functionals are also derived. Two equivalent expressions for the minimum free energy are given, one in terms of the history of strain and the other in terms of the minimal state variable. This latter quan- tity is also used to prove a theorem of existence and uniqueness of solutions of initial boundary value problems for incompressible fluids. Finally, the evo- lution of the system is described in terms of a strongly continuous semigroup of linear contraction operators on a suitable Hilbert space. Thus, a theorem of existence and uniqueness of solutions admitted by such an evolution problem is proved. Also, exponential decay of the associated e
2014
Some expressions for the free energy in the case of incompressible viscoelastic fluids are given. These are derived from free energies already introduced for other viscoelastic materials, adapted to incompressible fluids. A new free energy is given in terms of the minimal state descriptor. The internal dissipations related to these different functionals are also derived. Two equivalent expressions for the minimum free energy are given, one in terms of the history of strain and the other in terms of the minimal state variable. This latter quantity is also used to prove a theorem of existence and uniqueness of solutions to initial boundary value problems for incompressible fluids. Finally, the evolution of the system is described in terms of a strongly continuous semigroup of linear contraction operators on a suitable Hilbert space. Thus, a theorem of existence and uniqueness of solutions admitted by such an evolution problem is proved.
asymptotic behavior of solutions; fabrizio free energy; viscoelastic fluid; materials with memory; minimum free energy
01 Pubblicazione su rivista::01a Articolo in rivista
VISCOELASTIC FLUIDS: FREE ENERGIES, DIFFERENTIAL PROBLEMS AND ASYMPTOTIC BEHAVIOUR / Giovambattista, Amendola; Carillo, Sandra; John, Golden; Adele, Manes. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 19:7(2014), pp. 1815-1835. [10.3934/dcdsb.2014.19.1815]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/514586
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