In this paper we have proved exponential asymptotic stability for the corotational incompressible diffusive Johnson-Segalman viscolelastic model and a simple decay result for the corotational incompressible hyperbolic Maxwell model. Moreover we have established continuous dependence and uniqueness results for the non-zero equilibrium solution. In the compressible case, we have proved a Holder continuous dependence theorem upon the initial data and body force for both models, whence follows a result of continuous dependence on the initial data and, therefore, uniqueness. For the Johnson-Segalman model we have also dealt with the case of negative elastic viscosities, corresponding to retardation effects. A comparison with other type of viscoelasticity, showing short memory elastic effects, is given.

Uniqueness and stability results for non-linear Johnson-Segalman viscoelasticity and related models / Franca Franchi; Barbara Lazzari; Roberta Nibbi. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 19:7(2014), pp. 2111-2132. [10.3934/dcdsb.2014.19.2111]

Uniqueness and stability results for non-linear Johnson-Segalman viscoelasticity and related models

FRANCHI, FRANCA;LAZZARI, BARBARA;NIBBI, ROBERTA
2014

Abstract

In this paper we have proved exponential asymptotic stability for the corotational incompressible diffusive Johnson-Segalman viscolelastic model and a simple decay result for the corotational incompressible hyperbolic Maxwell model. Moreover we have established continuous dependence and uniqueness results for the non-zero equilibrium solution. In the compressible case, we have proved a Holder continuous dependence theorem upon the initial data and body force for both models, whence follows a result of continuous dependence on the initial data and, therefore, uniqueness. For the Johnson-Segalman model we have also dealt with the case of negative elastic viscosities, corresponding to retardation effects. A comparison with other type of viscoelasticity, showing short memory elastic effects, is given.
2014
Uniqueness and stability results for non-linear Johnson-Segalman viscoelasticity and related models / Franca Franchi; Barbara Lazzari; Roberta Nibbi. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 19:7(2014), pp. 2111-2132. [10.3934/dcdsb.2014.19.2111]
Franca Franchi; Barbara Lazzari; Roberta Nibbi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/338122
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