Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Acta Mechanica
Published in: Acta Mechanica 3/2020

17-12-2019 | Original Paper

Analyticity of solutions to thermoviscoelastic diffusion mixtures problem in higher dimension

Authors: Moncef Aouadi, Francesca Passarella, Vincenzo Tibullo

Published in: Acta Mechanica | Issue 3/2020

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we consider the linear theory of binary mixtures for thermoviscoelastic diffusion materials derived by Aouadi et al. (J Therm Stress 41:1414–1431, 2018). We establish the necessary and sufficient conditions to get a dissipation inequality for isotropic centrosymmetric materials. With the help of the semigroup theory of linear operators, we prove the well posedness of the higher-dimensional problem. Then, we show that the associated \(C_0\)-semigroup is analytic. Exponential stability and impossibility of localization of the solutions in time are immediate consequences.
previous article Nonlinear deformation and stress responses of a graded carbon nanotube sandwich plate structure under thermoelastic loading
next article Equivalence of Lagrange’s equations for non-material volume and the principle of virtual work in ALE formulation
Literature
1.
Alves, M.S., Muñoz Rivera, J.E., Quintanilla, R.: Exponential decay in a thermoelastic mixture of solids. Int. J. Solids Struct. 46, 1659–1666 (2009)MathSciNetCrossRef
2.
Alves, M.S., Muñoz Rivera, J.E., Sepúlveda, M., Vera Villagrán, O.P.: Analyticity of semigroups associated with thermoviscoelastic mixtures of solids. J. Therm. Stress. 32, 986–1004 (2009)CrossRef
3.
Alves, M.S., Sepulveda, M., Vera Villagran, O.P.: Stabilization of a system modeling temperature and porosity fields in a Kelvin–Voigt-type mixture. Acta Mech. 219, 145–167 (2011)CrossRef
4.
Alves, M.S., Muñoz Rivera, J.E., Sepúlveda, M., Vera Villagrán, O.P.: Stabilization in three-dimensional porous thermoviscoelastic mixtures. Quart. J. Math. 64, 37–57 (2013)MathSciNetCrossRef
5.
Alves, M.S., Muñoz Rivera, J.E., Sepúlveda, M., Vera, O.: About analyticity for the coupled system of linear thermoviscoelastic equations. Appl. Math. Comput. 270, 943–952 (2015)MathSciNetMATH
6.
Alves, M.S., Ferreira, M.V., Muñoz Rivera, J.E., Vera Villagrán, O.P.: Stability of a thermoelastic mixture with second sound. Math. Mech. Solids. 24, 1692–1706 (2018)MathSciNetCrossRef
7.
Aouadi, M.: Qualitative results in the theory of thermoelastic diffusion mixtures. J. Therm. Stress. 33, 595–615 (2010)CrossRef
8.
Aouadi, M.: Exponential stability in the theory of thermoelastic diffusion mixtures. Appl. Anal. 91, 2169–2187 (2012)MathSciNetCrossRef
9.
Aouadi, M., Ciarletta, M., Tibullo, V.: Well-posedness and exponential stability in binary mixtures theory for thermoviscoelastic diffusion materials. J. Therm. Stress. 41, 1414–1431 (2018)CrossRef
10.
Cordova Puma, F.F., Muñoz Rivera, J.E.: The lack of polynomial stability to mixtures with frictional dissipation. J. Math. Anal. Appl. 446, 1882–1897 (2017)MathSciNetCrossRef
11.
Fatori, L.H., da Silvab, R.P.: Stability of solution for a mixture of thermoelastic of type III. Math. Meth. Appl. Sci. 40, 4211–4221 (2017)MathSciNetCrossRef
12.
Fernàndez Sare, H.D., Muñoz Rivera, J.E., Quintanilla, R.: On the rate of decay in interacting continua with memory. J. Differ. Equ. 251, 3583–3605 (2011)MathSciNetCrossRef
13.
Fernàndez, J.R., Magaña, A., Masid, M., Quintanilla, R.: On the viscoelastic mixtures of solids. Appl. Math Optim. 79, 309–326 (2019)MathSciNetCrossRef
14.
Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin (1983)CrossRef
15.
Huang, F.L.: Strong asymptotic stability of linear dynamical systems in Banach spaces. J. Differ. Equ. 104, 307–324 (1993)MathSciNetCrossRef
16.
17.
Ieşan, D., Nappa, L.: On the theory of viscoelastic mixtures and stability. Math. Mech. Solids. 13, 55–80 (2008)MathSciNetCrossRef
18.
Ieşan, D., Quintanilla, R.: A Theory of porous thermoviscoelastic mixtures. J. Therm. Stress. 30, 693–714 (2007)MathSciNetCrossRef
19.
Ieşan, D., Scalia, A.: Thermoelastic Deformations. Kluwer Academic, Dordrecht (1996)CrossRef
20.
Ieşan, D., Scalia, A.: On a theory of thermoviscoelastic mixtures. J. Therm. Stress. 34, 228–243 (2011)CrossRef
21.
Liu, Z., Zheng, S.: Semigroups associated with dissipative systems. In: CRC Research Notes in Mathematics, Volume 398. Chapman & Hall, Boca Raton (1999)
22.
Magaña, A., Quintanilla, R.: On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity. J. Math. Anal. Appl. 412, 109–120 (2014)MathSciNetCrossRef
23.
Muñoz Rivera, J.E., Naso, M.G., Quintanilla, R.: Decay of solutions for a mixture of thermoelastic solids with different temperatures. Comput. Math. Appl. 71, 991–1009 (2016)MathSciNetCrossRef
24.
Nowacki, W.: Dynamical problems of thermoelastic diffusion in solids I. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 22, 55–64 (1974)
25.
Nowacki, W.: Dynamical problems of thermoelastic diffusion in solids II. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 22, 129–135 (1974)
26.
Onsager, L.: Reciprocal relations in irreversible processes. Phys. Rev. 37, 405–426 (1931)CrossRef
27.
Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1993)MATH
28.
Quintanilla, R.: Existence and exponential decay in the linear theory of viscoelastic mixtures. Eur. J. Mech. A Solids 24, 311–324 (2005)MathSciNetCrossRef
29.
Quintanilla, R.: Exponential decay in mixtures with localized dissipative term. Appl. Math. Lett. 18, 1381–1388 (2006)MathSciNetCrossRef
Metadata
Title
Analyticity of solutions to thermoviscoelastic diffusion mixtures problem in higher dimension
Authors
Moncef Aouadi
Francesca Passarella
Vincenzo Tibullo
Publication date
17-12-2019
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 3/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02572-y

Other articles of this Issue 3/2020

Acta Mechanica 3/2020 Go to the issue

Original Paper

Nonlinear modeling, dynamics, and chaos in a large deflection model of a rotor–disk–bearing system under geometric eccentricity and mass unbalance

Original Paper

Numerical simulation of conducting droplet impact on a surface under an electric field

Original Paper

Continuous and discontinuous contact problems of a homogeneous piezoelectric layer pressed by a conducting rigid flat punch

Original Paper

Anti-plane crack problem of a functionally graded piezoelectric materials strip with arbitrarily distributed properties

Original Paper

Existence of second spectrums of Timoshenko beam and Mindlin–Herrmann rod theories on the basis of atomistic studies

Original Paper

Thermoelastic responses of a finite rod due to nonlocal heat conduction

Premium Partners

    Image Credits