메뉴 건너뛰기




Volumn 61, Issue 4, 2003, Pages 759-781

Global solvability of a dissipative Frémond model for shape memory alloys. Part I: Mathematical formulation and uniqueness

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONTINUUM MECHANICS; INITIAL VALUE PROBLEMS; MARTENSITIC TRANSFORMATIONS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; SHAPE MEMORY EFFECT; TENSORS; THEOREM PROVING; THERMODYNAMICS; VECTORS;

EID: 0347682146     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/2019622     Document Type: Article
Times cited : (17)

References (36)
  • 2
    • 0000223804 scopus 로고
    • Sulle equazioni differenziali astratte del primo e del secondo ordine negli spazi di Hilbert
    • C. Baiocchi Sulle equazioni differenziali astratte del primo e del secondo ordine negli spazi di Hilbert, Ann. Mat. Pura Appl., (4), 76, 233-304 (1967)
    • (1967) Ann. Mat. Pura Appl. , vol.76 , Issue.4 , pp. 233-304
    • Baiocchi, C.1
  • 3
    • 0003478998 scopus 로고
    • Nonlinear semigroups and differential equations in Banach spaces
    • Noordhoff, Leyden, 1976
    • V. Barbu Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976
    • (1976)
    • Barbu, V.1
  • 4
    • 0007042823 scopus 로고    scopus 로고
    • Existence, uniqueness, and long time behavior for a nonlinear Volterra integrodifferential equation
    • V. Barbu, P. Colli, G. Gilardi, and M. Grasselli Existence, uniqueness, and long time behavior for a nonlinear Volterra integrodifferential equation, Differential Integral Equations, 13, 1233-1262 (2000)
    • (2000) Differential Integral Equations , vol.13 , pp. 1233-1262
    • Barbu, V.1    Colli, P.2    Gilardi, G.3    Grasselli, M.4
  • 6
    • 0035501722 scopus 로고    scopus 로고
    • Global solution to a Frémond model for shape memory alloys with thermal memory
    • E. Bonetti Global solution to a Frémond model for shape memory alloys with thermal memory, Nonlinear Anal., 46, 535-565 (2001)
    • (2001) Nonlinear Anal. , vol.46 , pp. 535-565
    • Bonetti, E.1
  • 7
    • 0038525450 scopus 로고    scopus 로고
    • Global solution to a nonlinear phase transition model with dissipation
    • E. Bonetti Global solution to a nonlinear phase transition model with dissipation, Adv. Math. Sci. Appl., 12, 355-376 (2002)
    • (2002) Adv. Math. Sci. Appl. , vol.12 , pp. 355-376
    • Bonetti, E.1
  • 8
    • 0011661684 scopus 로고    scopus 로고
    • Uniqueness results for the full Frémond model of shape memory alloys
    • N. Chemetov Uniqueness results for the full Frémond model of shape memory alloys, Z. Anal. Anwendungen, 17, 877-892 (1998)
    • (1998) Z. Anal. Anwendungen , vol.17 , pp. 877-892
    • Chemetov, N.1
  • 9
    • 0012607270 scopus 로고
    • Mathematical elasticity, vol. I: Three-dimensional elasticity
    • North-Holland, Amsterdam
    • P. G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity, in: Studies in Mathematics and its Applications, North-Holland, Amsterdam, 1988
    • (1988) Studies in Mathematics and Its Applications
    • Ciarlet, P.G.1
  • 10
    • 0000442141 scopus 로고
    • Global existence for the three-dimensional Frémond model of shape memory alloys
    • P. Coli Global existence for the three-dimensional Frémond model of shape memory alloys, Nonlinear Anal., 24, 1565-1579, (1995)
    • (1995) Nonlinear Anal. , vol.24 , pp. 1565-1579
    • Coli, P.1
  • 11
    • 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, 31-47 (1990)
    • (1990) Quart. Appl. Math. , vol.48 , pp. 31-47
    • Colli, P.1    Frémond, M.2    Visintin, A.3
  • 12
    • 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, 255-264 (1993)
    • (1993) Contin. Mech. Thermodyn. , vol.5 , pp. 255-264
    • Colli, P.1    Sprekels, J.2
  • 13
    • 0029288569 scopus 로고
    • Global solution to the full one-dimensional Frémond model for shape memory alloys
    • P. Colli and J. Sprekels Global solution to the full one-dimensional Frémond model for shape memory alloys, Math. Methods Appl. Sci., 18, 371-385 (1995)
    • (1995) Math. Methods Appl. Sci. , vol.18 , pp. 371-385
    • Colli, P.1    Sprekels, J.2
  • 14
    • 21444441775 scopus 로고    scopus 로고
    • Remarks on the existence for the one-dimensional Frémond model of shape memory alloys
    • P. Colli and J. Sprekels Remarks on the existence for the one-dimensional Frémond model of shape memory alloys, Z. Angew. Math. Mech., 76, Suppl. 2, 413-416 (1996)
    • (1996) Z. Angew. Math. Mech. , vol.76 , Issue.SUPPL. 2 , pp. 413-416
    • Colli, P.1    Sprekels, J.2
  • 15
    • 0004072908 scopus 로고
    • Inequalities in mechanics and physics
    • Springer-Verlag, Berlin-New York
    • G. Duvant and J. L. Lions Inequalities in mechanics and physics, Springer-Verlag, Berlin-New York, 1976
    • (1976)
    • Duvant, G.1    Lions, J.L.2
  • 16
    • 0003372616 scopus 로고    scopus 로고
    • Elastic phase transitions and nonconvex energy functions
    • (K. H. Hoffmann and J. Sprekels, eds.)
    • F. Falk Elastic phase transitions and nonconvex energy functions, in: "Free Boundary Problems: theory and applications", vol. I-II (K. H. Hoffmann and J. Sprekels, eds.)
    • Free Boundary Problems: Theory and Applications , vol.1-2
    • Falk, F.1
  • 19
    • 0001032360 scopus 로고    scopus 로고
    • Shape memory alloys. A thermomechanical model
    • (K. H. Hoffmann and J. Sprekels, eds.)
    • M. Frémond Shape memory alloys. A thermomechanical model, in "Free Boundary Problems: theory and applications", vol. I-II (K. H. Hoffmann and J. Sprekels, eds.)
    • Free Boundary Problems: Theory and Applications , vol.1-2
    • Frémond, M.1
  • 21
    • 0038525454 scopus 로고
    • Sur l'inégalité de Clausius-Duhem
    • M. Frémond Sur l'inégalité de Clausius-Duhem, C. R. Acad. Sci. Sér. II Paris, 311, 757-762 (1990)
    • (1990) C. R. Acad. Sci. Sér. II Paris , vol.311 , pp. 757-762
    • Frémond, M.1
  • 23
    • 3543057311 scopus 로고    scopus 로고
    • Nonsmooth thermo-mechanics
    • Springer-Verlag, Heidelberg
    • M. Frémond Nonsmooth thermo-mechanics, Springer-Verlag, Heidelberg, 2001
    • (2001)
    • Frémond, M.1
  • 24
  • 26
    • 0003980436 scopus 로고
    • Cours de mécanique des milieux continus
    • Masson, Paris
    • P. Germain Cours de mécanique des milieux continus, Masson, Paris, 1973
    • (1973)
    • Germain, P.1
  • 28
    • 26144438383 scopus 로고
    • Alliages à memoire de forme
    • Techniques de l'ingénieur, M530, Paris
    • G. Guénin Alliages à memoire de forme, Techniques de l'ingénieur, M530, Paris, 1986
    • (1986)
    • Guénin, G.1
  • 30
    • 0001098416 scopus 로고
    • Sur les lois de frottement, de viscosité et de plasticité
    • Paris
    • J. J. Moreau Sur les lois de frottement, de viscosité et de plasticité, in: C. R. Acad. Sci., 27, 608-611, Paris, 1970
    • (1970) C. R. Acad. Sci. , vol.27 , pp. 608-611
    • Moreau, J.J.1
  • 32
    • 51649158231 scopus 로고
    • A model for phase transitions in pseudoelastic bodies
    • I. Müller and K. Wilmanski A model for phase transitions in pseudoelastic bodies, Nuovo Cimento B, 57, 283-318 (1980).
    • (1980) Nuovo Cimento B , vol.57 , pp. 283-318
    • Müller, I.1    Wilmanski, K.2
  • 33
    • 0024052595 scopus 로고
    • Existence of a solution for a mathematical model of structural phase transition in shape memory alloys
    • M. Niezgódka and J. Sprekels Existence of a solution for a mathematical model of structural phase transition in shape memory alloys, Math. Methods Appl. Sci., 10, 197-223 (1988)
    • (1988) Math. Methods Appl. Sci. , vol.10 , pp. 197-223
    • Niezgódka, M.1    Sprekels, J.2
  • 34
    • 0344864845 scopus 로고
    • Les alliages à mémoire de forme
    • Hermès, Paris
    • E. Patoor and M. Berveiller Les alliages à mémoire de forme, Hermès, Paris, 1990
    • (1990)
    • Patoor, E.1    Berveiller, M.2
  • 35
    • 0001459585 scopus 로고    scopus 로고
    • Existence result for the full one-dimensional Frémond model of shape memory alloys
    • N. Shemetov Existence result for the full one-dimensional Frémond model of shape memory alloys, Adv. Math. Sci. Appl., 8, 157-172 (1998)
    • (1998) Adv. Math. Sci. Appl. , vol.8 , pp. 157-172
    • Shemetov, N.1
  • 36
    • 0000024345 scopus 로고
    • Shape memory alloys: Mathematical models for a class of first order solid-solid phase transitions in metals
    • J. Sprekels Shape memory alloys: mathematical models for a class of first order solid-solid phase transitions in metals, Control Cybernet., 19, 287-308 (1990)
    • (1990) Control Cybernet. , vol.19 , pp. 287-308
    • Sprekels, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.