메뉴 건너뛰기




Volumn 380, Issue 1, 2011, Pages 188-203

Well posedness of a linearized fractional derivative fluid model

Author keywords

Hadamard stability analysis; Objective fractional derivative constitutive equation; Rest state stability analysis; Smoothness; Solution existence; Uniqueness; Viscoelasticity

Indexed keywords


EID: 79953689576     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2011.02.047     Document Type: Article
Times cited : (24)

References (49)
  • 1
    • 0242667817 scopus 로고    scopus 로고
    • Fractional derivative viscoelasticity at large deformations
    • Adolfsson K., Enelund M. Fractional derivative viscoelasticity at large deformations. Nonlinear Dynam. 2003, 33:301-321.
    • (2003) Nonlinear Dynam. , vol.33 , pp. 301-321
    • Adolfsson, K.1    Enelund, M.2
  • 2
    • 15544363375 scopus 로고    scopus 로고
    • Nonlinear fractional order viscoelasticity at large strains
    • Adolfsson K. Nonlinear fractional order viscoelasticity at large strains. Nonlinear Dynam. 2004, 38:233-246.
    • (2004) Nonlinear Dynam. , vol.38 , pp. 233-246
    • Adolfsson, K.1
  • 4
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • Agarwal R.P., Benchohra M., Hamani S. A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 2010, 109:973-1033.
    • (2010) Acta Appl. Math. , vol.109 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 5
    • 0036650559 scopus 로고    scopus 로고
    • Solution for a fractional diffusion-wave equation defined in a bounded domain
    • Agrawall O.P. Solution for a fractional diffusion-wave equation defined in a bounded domain. Nonlinear Dynam. 2002, 29:145-155.
    • (2002) Nonlinear Dynam. , vol.29 , pp. 145-155
    • Agrawall, O.P.1
  • 6
    • 33750541076 scopus 로고    scopus 로고
    • Fractional Hamiltonian analysis of higher order derivatives systems
    • Baleanu D., Muslih S.I., Tas K. Fractional Hamiltonian analysis of higher order derivatives systems. J. Math. Phys. 2006, 47:103503.
    • (2006) J. Math. Phys. , vol.47 , pp. 103503
    • Baleanu, D.1    Muslih, S.I.2    Tas, K.3
  • 8
    • 0004143319 scopus 로고
    • Analyse mathématique et calcul numérique pour les sciences et les techniques, vol. 8, Evolution: semi-groupe, variationnel
    • Masson, Paris
    • Dautray R., Lions J.-L. Analyse mathématique et calcul numérique pour les sciences et les techniques, vol. 8, Evolution: semi-groupe, variationnel. INSTN CEA Collect. Enseign. 1988, Masson, Paris.
    • (1988) INSTN CEA Collect. Enseign.
    • Dautray, R.1    Lions, J.-L.2
  • 9
    • 21944431546 scopus 로고    scopus 로고
    • Some applications of fractional calculus to polymer science
    • Douglas J.F. Some applications of fractional calculus to polymer science. Adv. Chem. Phys. 1997, 102:121.
    • (1997) Adv. Chem. Phys. , vol.102 , pp. 121
    • Douglas, J.F.1
  • 10
    • 0002760993 scopus 로고    scopus 로고
    • Polymer science applications of path-integration, integral equations, and fractional calculus
    • World Scientific, Singapore, R. Hilfer (Ed.)
    • Douglas J.F. Polymer science applications of path-integration, integral equations, and fractional calculus. Applications of Fractional Calculus in Physics 2000, World Scientific, Singapore. R. Hilfer (Ed.).
    • (2000) Applications of Fractional Calculus in Physics
    • Douglas, J.F.1
  • 11
    • 0031359852 scopus 로고    scopus 로고
    • Fractional differential models in finite viscoelasticity
    • Drozdov A.D. Fractional differential models in finite viscoelasticity. Acta Mech. 1997, 124:155-180.
    • (1997) Acta Mech. , vol.124 , pp. 155-180
    • Drozdov, A.D.1
  • 12
    • 0002717771 scopus 로고
    • Relaxation functions of rheological constitutive equations with fractional derivatives: Thermodynamical constraints
    • Springer-Verlag, New York
    • Friedrich C. Relaxation functions of rheological constitutive equations with fractional derivatives: Thermodynamical constraints. Lecture Notes in Phys. 1991, vol. 381. Springer-Verlag, New York.
    • (1991) Lecture Notes in Phys. , vol.381
    • Friedrich, C.1
  • 13
    • 47249162373 scopus 로고    scopus 로고
    • Time fractional derivatives for voltage creep in ferroelectric materials: theory and experiment
    • Guyomar D., Ducharne B., Sébald G. Time fractional derivatives for voltage creep in ferroelectric materials: theory and experiment. J. Phys. D: Appl. Phys. 2008, 41:125410.
    • (2008) J. Phys. D: Appl. Phys. , vol.41 , pp. 125410
    • Guyomar, D.1    Ducharne, B.2    Sébald, G.3
  • 14
    • 34250319419 scopus 로고    scopus 로고
    • Fractional-order relaxation laws in non-linear viscoelasticity
    • Hanyga A. Fractional-order relaxation laws in non-linear viscoelasticity. Contin. Mech. Thermodyn. 2007, 19:25-36.
    • (2007) Contin. Mech. Thermodyn. , vol.19 , pp. 25-36
    • Hanyga, A.1
  • 15
    • 43049083704 scopus 로고    scopus 로고
    • On the rest state stability of an objective fractional derivative viscoelastic fluid model
    • Heibig A., Palade L.I. On the rest state stability of an objective fractional derivative viscoelastic fluid model. J. Math. Phys. 2008, 49:043101.
    • (2008) J. Math. Phys. , vol.49 , pp. 043101
    • Heibig, A.1    Palade, L.I.2
  • 18
    • 33745015093 scopus 로고    scopus 로고
    • Computational modelling of thermoforming processes in the case of finite viscoelastic materials
    • Karamanou M., Warby M.K., Whiteman J.R. Computational modelling of thermoforming processes in the case of finite viscoelastic materials. Comput. Methods Appl. Mech. Engrg. 2006, 195:5220.
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 5220
    • Karamanou, M.1    Warby, M.K.2    Whiteman, J.R.3
  • 20
    • 10844264077 scopus 로고    scopus 로고
    • Fractional Brownian dynamics in proteins
    • Kneller G.R., Hinsen K. Fractional Brownian dynamics in proteins. J. Chem. Phys. 2004, 121:10278-10283.
    • (2004) J. Chem. Phys. , vol.121 , pp. 10278-10283
    • Kneller, G.R.1    Hinsen, K.2
  • 21
    • 77955262712 scopus 로고    scopus 로고
    • A theory relating creep and relaxation for linear materials with memory
    • Koeller R.C. A theory relating creep and relaxation for linear materials with memory. Trans. ASME J. Appl. Mech. 2010, 77:031008.
    • (2010) Trans. ASME J. Appl. Mech. , vol.77 , pp. 031008
    • Koeller, R.C.1
  • 22
    • 0031285474 scopus 로고    scopus 로고
    • On the thermodynamics of fractional damping elements
    • Lion A. On the thermodynamics of fractional damping elements. Contin. Mech. Thermodyn. 1997, 9:83.
    • (1997) Contin. Mech. Thermodyn. , vol.9 , pp. 83
    • Lion, A.1
  • 24
    • 15044362199 scopus 로고    scopus 로고
    • A fractional equation for anomalous diffusion in a randomly heterogeneous porous medium
    • Logvinova K., Neel M.C. A fractional equation for anomalous diffusion in a randomly heterogeneous porous medium. Chaos 2004, 14:982-987.
    • (2004) Chaos , vol.14 , pp. 982-987
    • Logvinova, K.1    Neel, M.C.2
  • 26
    • 0000287571 scopus 로고    scopus 로고
    • Three-dimensional constitutive viscoelastic laws with fractional order time derivatives
    • Makris N. Three-dimensional constitutive viscoelastic laws with fractional order time derivatives. J. Rheol. 1997, 41:1007.
    • (1997) J. Rheol. , vol.41 , pp. 1007
    • Makris, N.1
  • 29
    • 50049102930 scopus 로고    scopus 로고
    • Fractional diffusion-wave problem in cylindrical coordinates
    • Özdemir N., Karadeniz D. Fractional diffusion-wave problem in cylindrical coordinates. Phys. Lett. A 2008, 372:5968-5972.
    • (2008) Phys. Lett. A , vol.372 , pp. 5968-5972
    • Özdemir, N.1    Karadeniz, D.2
  • 30
    • 0000533981 scopus 로고
    • Time-temperature superposition and linear viscoelasticity of polybutadienes
    • Palade L.I., Verney V., Attané P. Time-temperature superposition and linear viscoelasticity of polybutadienes. Macromol. 1995, 28:7051-7057.
    • (1995) Macromol. , vol.28 , pp. 7051-7057
    • Palade, L.I.1    Verney, V.2    Attané, P.3
  • 31
    • 5544323641 scopus 로고    scopus 로고
    • A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime
    • Palade L.I., Verney V., Attané P. A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime. Rheol. Acta 1996, 35:265.
    • (1996) Rheol. Acta , vol.35 , pp. 265
    • Palade, L.I.1    Verney, V.2    Attané, P.3
  • 32
    • 0000756969 scopus 로고    scopus 로고
    • Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models
    • Palade L.I., Attané P., Huilgol R.R., Mena B. Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models. Internat. J. Engrg. Sci. 1999, 37:315.
    • (1999) Internat. J. Engrg. Sci. , vol.37 , pp. 315
    • Palade, L.I.1    Attané, P.2    Huilgol, R.R.3    Mena, B.4
  • 33
    • 0038824732 scopus 로고    scopus 로고
    • A new constitutive equation that models extensional flow strain hardening based on evolving natural configurations: stability analysis
    • Palade L.I., Walton J.R., Farina A. A new constitutive equation that models extensional flow strain hardening based on evolving natural configurations: stability analysis. Internat. J. Non-Linear Mech. 2004, 39:379-387.
    • (2004) Internat. J. Non-Linear Mech. , vol.39 , pp. 379-387
    • Palade, L.I.1    Walton, J.R.2    Farina, A.3
  • 34
    • 1442358002 scopus 로고    scopus 로고
    • An integral constitutive law for viscoelastic fluids based on the concept of evolving natural configurations: stability analysis
    • Palade L.I. An integral constitutive law for viscoelastic fluids based on the concept of evolving natural configurations: stability analysis. Internat. J. Non-Linear Mech. 2004, 39:1275-1287.
    • (2004) Internat. J. Non-Linear Mech. , vol.39 , pp. 1275-1287
    • Palade, L.I.1
  • 36
    • 33644608434 scopus 로고    scopus 로고
    • Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers
    • Robertson C.G., Palade L.I. Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers. J. Non-Cryst. Solids 2006, 352:342-348.
    • (2006) J. Non-Cryst. Solids , vol.352 , pp. 342-348
    • Robertson, C.G.1    Palade, L.I.2
  • 37
    • 43049126046 scopus 로고    scopus 로고
    • A composition rule to predict the linear viscoelastic properties of polybutadienes with varying microstructure
    • Robles-Vasquez O., Gonzalez-Alvarez A., Puig J.E., Manero O. A composition rule to predict the linear viscoelastic properties of polybutadienes with varying microstructure. Rubber Chem. Technol. 2006, 79:859-869.
    • (2006) Rubber Chem. Technol. , vol.79 , pp. 859-869
    • Robles-Vasquez, O.1    Gonzalez-Alvarez, A.2    Puig, J.E.3    Manero, O.4
  • 39
    • 21144450704 scopus 로고    scopus 로고
    • Nonlinear differential equations with fractional damping with applications to the 1dof and 2dof pendulum
    • Seredyńska M., Hanyga A. Nonlinear differential equations with fractional damping with applications to the 1dof and 2dof pendulum. Acta Mech. 2005, 176:169-183.
    • (2005) Acta Mech. , vol.176 , pp. 169-183
    • Seredyńska, M.1    Hanyga, A.2
  • 40
    • 10144259398 scopus 로고    scopus 로고
    • A posteriori error estimates for space-time finite element approximation of quasistatic hereditary linear viscoelasticity problems
    • Shaw S., Whiteman J.R. A posteriori error estimates for space-time finite element approximation of quasistatic hereditary linear viscoelasticity problems. Comput. Methods Appl. Mech. Engrg. 2004, 193:5551.
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 5551
    • Shaw, S.1    Whiteman, J.R.2
  • 41
    • 0034352042 scopus 로고    scopus 로고
    • Adaptive space-time finite element solution for Volterra equations arising in viscoelasticity problems
    • Shaw S., Whiteman J.R. Adaptive space-time finite element solution for Volterra equations arising in viscoelasticity problems. J. Comput. Appl. Math. 2000, 125:337.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 337
    • Shaw, S.1    Whiteman, J.R.2
  • 42
    • 0031337669 scopus 로고    scopus 로고
    • Applications and numerical analysis of partial differential Volterra equations: A brief survey
    • Shaw S., Whiteman J.R. Applications and numerical analysis of partial differential Volterra equations: A brief survey. Comput. Methods Appl. Mech. Engrg. 1997, 150:397.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.150 , pp. 397
    • Shaw, S.1    Whiteman, J.R.2
  • 43
    • 0037410852 scopus 로고    scopus 로고
    • A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates
    • Tan W.C., Pan W.X., Xu M.Y. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. Internat. J. Non-Linear Mech. 2003, 38:645-650.
    • (2003) Internat. J. Non-Linear Mech. , vol.38 , pp. 645-650
    • Tan, W.C.1    Pan, W.X.2    Xu, M.Y.3
  • 44
    • 0003246899 scopus 로고    scopus 로고
    • Infinite-Dimensional Dynamical Systems in Mechanics and Physics
    • Springer-Verlag, New York
    • Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Appl. Math. Sci. 1997, vol. 68. Springer-Verlag, New York.
    • (1997) Appl. Math. Sci. , vol.68
    • Temam, R.1
  • 45
    • 67649429378 scopus 로고    scopus 로고
    • On Hadamard stability and dissipative stability of the molecular stress function model of non-linear viscoelasticity
    • Voyiatzis E., Tsenoglu C.J., Boudouvis A.G. On Hadamard stability and dissipative stability of the molecular stress function model of non-linear viscoelasticity. Internat. J. Non-Linear Mech. 2009, 44:727-734.
    • (2009) Internat. J. Non-Linear Mech. , vol.44 , pp. 727-734
    • Voyiatzis, E.1    Tsenoglu, C.J.2    Boudouvis, A.G.3
  • 47
    • 55549139469 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional partial differential equations with the homotopy analysis method
    • Xu H., Liao S.-J., You X.-C. Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 2009, 14:1152-1156.
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 1152-1156
    • Xu, H.1    Liao, S.-J.2    You, X.-C.3
  • 48
    • 77957328858 scopus 로고    scopus 로고
    • Start-up flow of a viscoelastic fluid in a pipe with a fractional Maxwell's model
    • Yang D., Zhu K.Q. Start-up flow of a viscoelastic fluid in a pipe with a fractional Maxwell's model. Comput. Math. Appl. 2010, 60:2231.
    • (2010) Comput. Math. Appl. , vol.60 , pp. 2231
    • Yang, D.1    Zhu, K.Q.2
  • 49
    • 32144446304 scopus 로고    scopus 로고
    • Oscillating flow of a viscoelastic fluid in a pipe with the fractional Maxwell model
    • Yin Y.B., Zhu K.Q. Oscillating flow of a viscoelastic fluid in a pipe with the fractional Maxwell model. Appl. Math. Comput. 2006, 173:231-242.
    • (2006) Appl. Math. Comput. , vol.173 , pp. 231-242
    • Yin, Y.B.1    Zhu, K.Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.