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 eI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.