메뉴 건너뛰기




Volumn , Issue 406, 2002, Pages 5-46

Existence and uniqueness of solutions for a three-dimensional thermoelastic system

Author keywords

Nonlinear thermoelasticity; Parabolic regularization; Shape memory alloys

Indexed keywords


EID: 25144465579     PISSN: 00123862     EISSN: 17306310     Source Type: Journal    
DOI: 10.4064/dm406-0-1     Document Type: Article
Times cited : (24)

References (55)
  • 1
    • 0026237436 scopus 로고
    • Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids
    • R. Abeyaratne and J. K. Knowles, Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids, SIAM J. Appl. Math. 51 (1991), 1205-1221.
    • (1991) SIAM J. Appl. Math , vol.51 , pp. 1205-1221
    • Abeyaratne, R.1    Knowles, J.K.2
  • 2
    • 0347394179 scopus 로고    scopus 로고
    • On the entropy principle of phase transition models with a conserved order parameter
    • H. W. Alt and I. Pawłow, On the entropy principle of phase transition models with a conserved order parameter, Adv. Math. Sci. Appl. 6 (1996), 291-376.
    • (1996) Adv. Math. Sci. Appl , vol.6 , pp. 291-376
    • Alt, H.W.1    Pawłow, I.2
  • 5
    • 0001265315 scopus 로고
    • Twin boundaries in ferroelastic media without interface dislocations
    • G. R. Barsch and J. A. Krumhansl, Twin boundaries in ferroelastic media without interface dislocations, Phys. Rev. Lett. 53 (1984), 1069-1072.
    • (1984) Phys. Rev. Lett , vol.53 , pp. 1069-1072
    • Barsch, G.R.1    Krumhansl, J.A.2
  • 8
    • 0000442141 scopus 로고
    • Global existence for the three-dimensional Frémond model of shape memory alloys
    • P. Colli, Global existence for the three-dimensional Frémond model of shape memory alloys, Nonlinear Anal. 24 (1995), 1565-1579.
    • (1995) Nonlinear Anal , vol.24 , pp. 1565-1579
    • Colli, P.1
  • 9
    • 0025399031 scopus 로고
    • Thermo-mechanical evolution of shape memory alloys
    • P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys, Quart. Appl. Math. 48 (1990), 31-47.
    • (1990) Quart. Appl. Math , vol.48 , pp. 31-47
    • Colli, P.1    Frémond, M.2    Visintin, A.3
  • 10
    • 0000416424 scopus 로고
    • Global existence for the three-dimensional model for the thermo-mechanical evolution of shape memory alloys
    • P. Colli and J. Sprekels, Global existence for the three-dimensional model for the thermo-mechanical evolution of shape memory alloys, Nonlinear Anal. 18 (1992), 873-888.
    • (1992) Nonlinear Anal , vol.18 , pp. 873-888
    • Colli, P.1    Sprekels, J.2
  • 11
    • 0001000937 scopus 로고
    • Positivity of temperature in the general Frémond model for shape memory alloys
    • P. Colli and J. Sprekels, Positivity of temperature in the general Frémond model for shape memory alloys, Contin. Mech. Thermodyn. 5 (1993), 255-264.
    • (1993) Contin. Mech. Thermodyn , vol.5 , pp. 255-264
    • Colli, P.1    Sprekels, J.2
  • 12
    • 0000367902 scopus 로고
    • Global smooth thermomechanical processes in one-dimen-sional nonlinear thermoviscoelasticity
    • C. M. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimen-sional nonlinear thermoviscoelasticity, Nonlinear Anal. 6 (1982), 435-454.
    • (1982) Nonlinear Anal , vol.6 , pp. 435-454
    • Dafermos, C.M.1    Hsiao, L.2
  • 14
    • 0021788792 scopus 로고
    • On the thermomechanics of interstitial working
    • J. E. Dunn and J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal. 88 (1985), 95-133.
    • (1985) Arch. Rational Mech. Anal , vol.88 , pp. 95-133
    • Dunn, J.E.1    Serrin, J.2
  • 15
    • 0015728267 scopus 로고
    • On the existence of symmetry relations and dissipation potentials
    • D. G. B. Edelen, On the existence of symmetry relations and dissipation potentials, Arch. Rational Mech. Anal. 88 (1985), 51 (1973), 218-227.
    • (1973) Arch. Rational Mech. Anal. 88 (1985) , vol.51 , pp. 218-227
    • Edelen, D.G.B.1
  • 16
    • 84893474234 scopus 로고
    • 63, in: Partial Differential Equations VI, Encyclopaedia Math. Sci. Yu. V. Egorov and M.A. Shubin (eds.), Springer
    • S. D. Ejdelman, Parabolic equations, in: Partial Differential Equations VI, Encyclopaedia Math. Sci. 63, Yu. V. Egorov and M. A. Shubin (eds.), Springer, 1994, 205-316.
    • (1994) Parabolic equations , pp. 205-316
    • Ejdelman, S.D.1
  • 17
    • 0022906928 scopus 로고
    • Constitutive theory for some constrained elastic crystals
    • J. L. Ericksen, Constitutive theory for some constrained elastic crystals, Internat. J. Solids Structures 22 (1986), 951-964.
    • (1986) Internat. J. Solids Structures , vol.22 , pp. 951-964
    • Ericksen, J.L.1
  • 18
    • 0020251025 scopus 로고
    • Landau theory and martensitic phase transitions
    • F. Falk, Landau theory and martensitic phase transitions, J. Physique C4 43 (1982), 3-15.
    • (1982) J. Physique C4 , vol.43 , pp. 3-15
    • Falk, F.1
  • 19
    • 84893490105 scopus 로고
    • in: Free Boundary Problems: Theory and Applications, K.-H. Hoffmann and J. Sprekels (eds.), Vol. I, Longman, New York
    • F. Falk, Elastic phase transitions and nonconvex energy functions, in: Free Boundary Problems: Theory and Applications, K.-H. Hoffmann and J. Sprekels (eds.), Vol. I, Longman, New York, 1990, 45-55.
    • (1990) Elastic phase transitions and nonconvex energy functions , pp. 45-55
    • Falk, F.1
  • 20
    • 0002434735 scopus 로고
    • Three-dimensional Landau theory describing the martensitic phase transformation of shape memory alloys
    • F. Falk and P. Konopka, Three-dimensional Landau theory describing the martensitic phase transformation of shape memory alloys, J. Phys.: Condensed Matter 2 (1990), 61-77.
    • (1990) J. Phys.: Condensed Matter , vol.2 , pp. 61-77
    • Falk, F.1    Konopka, P.2
  • 21
    • 0032141408 scopus 로고    scopus 로고
    • On a model of nonlocal continuum mechanics Part I: Existence and regularity
    • R. L. Fosdick and D. E. Mason, On a model of nonlocal continuum mechanics Part I: Existence and regularity, SIAM J. Appl. Math. 58 (1998), 1278-1306.
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 1278-1306
    • Fosdick, R.L.1    Mason, D.E.2
  • 22
    • 0018292795 scopus 로고
    • On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids
    • R. L. Fosdick and J. Serrin, On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids, J. Elasticity 9 (1979), 83-89.
    • (1979) J. Elasticity , vol.9 , pp. 83-89
    • Fosdick, R.L.1    Serrin, J.2
  • 24
    • 26544469625 scopus 로고
    • Dynamic solid-solid transitions with phase characterized by an order parameter
    • E. Fried and M. E. Gurtin, Dynamic solid-solid transitions with phase characterized by an order parameter, Phys. D 72 (1994), 287-308.
    • (1994) Phys. D , vol.72 , pp. 287-308
    • Fried, E.1    Gurtin, M.E.2
  • 25
    • 84972553547 scopus 로고
    • Systems of nonlinear wave equations with nonlinear viscosity
    • A. Friedman and J. Něcas, Systems of nonlinear wave equations with nonlinear viscosity, Pacific J. Math. 135 (1988), 29-55.
    • (1988) Pacific J. Math , vol.135 , pp. 29-55
    • Friedman, A.1    Něcas, J.2
  • 26
    • 0031488286 scopus 로고    scopus 로고
    • Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy
    • G. Friesecke and G. Dolzmann, Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy, SIAM J. Math. Anal. 28 (1997), 363-380.
    • (1997) SIAM J. Math. Anal , vol.28 , pp. 363-380
    • Friesecke, G.1    Dolzmann, G.2
  • 27
    • 51249167631 scopus 로고
    • p Sobolev spaces
    • p Sobolev spaces, Math. Z. 218 (1995), 43-90.
    • (1995) Math. Z , vol.218 , pp. 43-90
    • Grubb, G.1
  • 29
    • 0000413574 scopus 로고
    • Existence and uniqueness of global solutions to an extended model of the dynamical developments in shape memory alloys
    • K.-H. Hoffmann, M. Niezgódka and S. Zheng, Existence and uniqueness of global solutions to an extended model of the dynamical developments in shape memory alloys, Nonlinear Anal. 15 (1990), 977-990.
    • (1990) Nonlinear Anal , vol.15 , pp. 977-990
    • Hoffmann, K.-H.1    Niezgódka, M.2    Zheng, S.3
  • 30
    • 84988147740 scopus 로고
    • Existence of solutions to some non-linear thermoelastic systems with viscosity
    • K.-H. Hoffmann and A. Żochowski, Existence of solutions to some non-linear thermoelastic systems with viscosity, Math. Methods Appl. Sci. 15 (1992), 187-204.
    • (1992) Math. Methods Appl. Sci , vol.15 , pp. 187-204
    • Hoffmann, K.-H.1    Zochowski, A.2
  • 31
    • 0000934468 scopus 로고
    • The computation of the dynamics of the martensitic transfor-mation
    • P. Klouček and M. Luskin, The computation of the dynamics of the martensitic transfor-mation, Contin. Mech. Thermodyn. 6 (1994), 209-240.
    • (1994) Contin. Mech. Thermodyn , vol.6 , pp. 209-240
    • Klouček, P.1    Luskin, M.2
  • 34
    • 0003391566 scopus 로고
    • Interaction of Mechanics and Mathematics Series, Pitman, Boston
    • I. Müller, Thermodynamics, Interaction of Mechanics and Mathematics Series, Pitman, Boston, 1985.
    • (1985) Thermodynamics
    • Müller, I.1
  • 37
    • 84985336412 scopus 로고
    • Uniqueness of solutions to the systems of thermoe-lastic bodies with strong viscosity
    • J. Něcas, A. Novotný and V. Šverák, Uniqueness of solutions to the systems of thermoe-lastic bodies with strong viscosity, Math. Nachr. 149 (1990), 319-324.
    • (1990) Math. Nachr , vol.149 , pp. 319-324
    • Něcas, J.1    Novotný, A.2    Šverák, V.3
  • 38
    • 0024052595 scopus 로고
    • Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys
    • M. Niezgodka and J. Sprekels, Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys, Math. Methods Appl. Sci. 10 (1988), 197-223.
    • (1988) Math. Methods Appl. Sci , vol.10 , pp. 197-223
    • Niezgodka, M.1    Sprekels, J.2
  • 39
    • 0347573291 scopus 로고    scopus 로고
    • Three-dimensional model of thermomechanical evolution of shape memory ma-terials
    • I. Pawłow, Three-dimensional model of thermomechanical evolution of shape memory ma-terials, Control Cybernet. 29 (2000), 341-365.
    • (2000) Control Cybernet , vol.29 , pp. 341-365
    • Pawłow, I.1
  • 40
    • 84893500292 scopus 로고    scopus 로고
    • in: Proc. Free Boundary Problems: Theory and Applications I, N. Kenmochi (ed.), Gakuto Internat. Ser. Math. Sci. Appl. 13
    • I. Pawłow and A. Żochowski, Nonlinear thermoelastic system with viscosity and nonlocal-ity, in: Proc. Free Boundary Problems: Theory and Applications I, N. Kenmochi (ed.), Gakuto Internat. Ser. Math. Sci. Appl. 13, 2000, 251-265.
    • (2000) Nonlinear thermoelastic system with viscosity and nonlocal-ity , pp. 251-265
    • Pawłow, I.1    Zochowski, A.2
  • 41
    • 0023170272 scopus 로고
    • Phase transitions in one-dimensional viscoelasticity: Admissibility and stability
    • R. Pego, Phase transitions in one-dimensional viscoelasticity: admissibility and stability, Arch. Rational Mech. Anal. 97 (1987), 353-394.
    • (1987) Arch. Rational Mech. Anal , vol.97 , pp. 353-394
    • Pego, R.1
  • 43
    • 84893508955 scopus 로고    scopus 로고
    • in: Lectures on Applied Mathematics, H.-J. Bungartz et al. C. Zenger (eds.), Springer, Berlin
    • T. Roubiček, Dissipative evolution of microstructure in shape memory alloys, in: Lectures on Applied Mathematics, H.-J. Bungartz et al. C. Zenger (eds.), Springer, Berlin, 1999, 45-63.
    • (1999) Dissipative evolution of microstructure in shape memory alloys , pp. 45-63
    • Roubiček, T.1
  • 44
    • 84974082050 scopus 로고
    • Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions
    • P. Rybka, Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), 101-138.
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.121 , pp. 101-138
    • Rybka, P.1
  • 45
    • 0346763736 scopus 로고
    • A priori estimates for the gradient of the solution to the system of viscoelasticity in several dimensions
    • P. Rybka, A priori estimates for the gradient of the solution to the system of viscoelasticity in several dimensions, Topol. Methods Nonlinear Anal. 3 (1994), 235-256.
    • (1994) Topol. Methods Nonlinear Anal , vol.3 , pp. 235-256
    • Rybka, P.1
  • 46
    • 21944446952 scopus 로고    scopus 로고
    • The viscous damping prevents propagation of singularities in the system of vis-coelasticity
    • P. Rybka, The viscous damping prevents propagation of singularities in the system of vis-coelasticity, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 1067-1074.
    • (1997) Proc. Roy. Soc. Edinburgh Sect. A , vol.127 , pp. 1067-1074
    • Rybka, P.1
  • 47
    • 0003086507 scopus 로고    scopus 로고
    • Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity
    • P. Rybka and K.-H. Hoffmann, Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity, J. Math. Anal. Appl. 226 (1998), 61-81.
    • (1998) J. Math. Anal. Appl , vol.226 , pp. 61-81
    • Rybka, P.1    Hoffmann, K.-H.2
  • 49
    • 24944483464 scopus 로고
    • On boundary value problems for general linear parabolic systems
    • (in Russian)
    • V. A. Solonnikov, On boundary value problems for general linear parabolic systems, Dokl. Akad. Nauk SSSR 157 (1964), 56-59 (in Russian).
    • (1964) Dokl. Akad. Nauk SSSR , vol.157 , pp. 56-59
    • Solonnikov, V.A.1
  • 50
    • 0024753762 scopus 로고
    • Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys
    • J. Sprekels and S. Zheng, Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys, Phys. D 39 (1989), 59-76.
    • (1989) Phys. D , vol.39 , pp. 59-76
    • Sprekels, J.1    Zheng, S.2
  • 51
    • 21144484260 scopus 로고
    • Energy minimization and the formation of microstructure in dynamic anti-plane shear
    • P. J. Swart and P. J. Holmes, Energy minimization and the formation of microstructure in dynamic anti-plane shear, Arch. Rational Mech. Anal. 121 (1992), 37-85.
    • (1992) Arch. Rational Mech. Anal , vol.121 , pp. 37-85
    • Swart, P.J.1    Holmes, P.J.2
  • 53
    • 0000355706 scopus 로고
    • About the "normal growth" approximation in the dynamical theory of phase transitions
    • L. Truskinovsky, About the "normal growth" approximation in the dynamical theory of phase transitions, Contin. Mech. Thermodyn. 6 (1994), 185-208.
    • (1994) Contin. Mech. Thermodyn , vol.6 , pp. 185-208
    • Truskinovsky, L.1
  • 55
    • 84893479513 scopus 로고
    • presentation at the 10th Conference on Problems and Methods in Mathematical Physics, September, Chemnitz, Germany
    • A. Żochowski, Regularity of solutions to certain viscosity systems, presentation at the 10th Conference on Problems and Methods in Mathematical Physics, September 13-17, 1993, Chemnitz, Germany.
    • (1993) Regularity of solutions to certain viscosity systems , pp. 13-17
    • Zochowski, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.