메뉴 건너뛰기




Volumn 48, Issue 1, 1997, Pages 51-100

On a Model of Nonlocal Continuum Mechanics. Part II: Structure, Asymptotics, and Computations

Author keywords

Calculus of variations; Nonlocality; Phase transformations

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; ELASTICITY; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; PHASE INTERFACES; PHASE TRANSITIONS; STRAIN; VARIATIONAL TECHNIQUES;

EID: 0031354694     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007411628062     Document Type: Article
Times cited : (7)

References (24)
  • 1
    • 0003513119 scopus 로고
    • Variational convergence for functions and operators
    • Pitman Adv. Publ. Program
    • H. Attouch, Variational convergence for functions and operators. Appl. Math. Series, Pitman Adv. Publ. Program, 1984.
    • (1984) Appl. Math. Series
    • Attouch, H.1
  • 2
    • 0000093666 scopus 로고
    • A version of the fundamental theorem of Young measure
    • Partial Differential Equations and Continuum Models of Phase Transitions, M. Rascle, D. Serre, and M. Slemrod (eds), Springer-Verlag
    • J.M. Ball, A version of the fundamental theorem of Young measure. In: Partial Differential Equations and Continuum Models of Phase Transitions, M. Rascle, D. Serre, and M. Slemrod (eds), Lecture Notes in Physics 344, 207-215. Springer-Verlag, 1989.
    • (1989) Lecture Notes in Physics , vol.344 , pp. 207-215
    • Ball, J.M.1
  • 3
    • 0002854369 scopus 로고
    • Proposed experimental tests of a theory of fine micro structure and the two well problem
    • J.M. Ball and R.D. James, Proposed experimental tests of a theory of fine micro structure and the two well problem. Phil. Trans. R. Soc. Lond. A, 338 (1992) 389-450.
    • (1992) Phil. Trans. R. Soc. Lond. A , vol.338 , pp. 389-450
    • Ball, J.M.1    James, R.D.2
  • 4
    • 84971972596 scopus 로고
    • The Cahn-Hilliard gradient theory for phase separation with nonsmooth free energy, Part I: Mathematical analysis
    • J.F. Blowey, and C.M. Elliot, The Cahn-Hilliard gradient theory for phase separation with nonsmooth free energy, Part I: Mathematical analysis. Euro. J. of Appl. Math. 2 (1991) 233-279.
    • (1991) Euro. J. of Appl. Math. , vol.2 , pp. 233-279
    • Blowey, J.F.1    Elliot, C.M.2
  • 5
    • 35949030317 scopus 로고
    • Modified van der Waals theory of fluid interfaces
    • V. Bongiorno, and H.T. Davis, Modified van der Waals theory of fluid interfaces. Phys. Rev. A, 12 (1975) 2213-2224.
    • (1975) Phys. Rev. A , vol.12 , pp. 2213-2224
    • Bongiorno, V.1    Davis, H.T.2
  • 8
    • 0019146946 scopus 로고
    • The morphology and stability of material phases
    • J.E. Dunn, and R.L. Fosdick, The morphology and stability of material phases. Arch. Rational Mech. Anal. 74 (1980) 1-99.
    • (1980) Arch. Rational Mech. Anal. , vol.74 , pp. 1-99
    • Dunn, J.E.1    Fosdick, R.L.2
  • 9
    • 0016569455 scopus 로고
    • Equilibrium of bars
    • J.L. Ericksen, Equilibrium of bars. J. Elasticity 5 (1975) 191-201.
    • (1975) J. Elasticity , vol.5 , pp. 191-201
    • Ericksen, J.L.1
  • 10
    • 0001429265 scopus 로고    scopus 로고
    • Single phase energy minimizers for materials with nonlocal spatial dependence
    • R.L. Fosdick and D.E. Mason, Single phase energy minimizers for materials with nonlocal spatial dependence. Quart. Appl. Math 54 (1996) 161-195.
    • (1996) Quart. Appl. Math , vol.54 , pp. 161-195
    • Fosdick, R.L.1    Mason, D.E.2
  • 11
    • 2342616006 scopus 로고    scopus 로고
    • Nonlocal continuum mechanics, Part I: Existence and regularity
    • To appear
    • R.L. Fosdick and D.E. Mason, Nonlocal continuum mechanics, Part I: Existence and regularity. SIAM J. Appl. Math. To appear.
    • SIAM J. Appl. Math
    • Fosdick, R.L.1    Mason, D.E.2
  • 13
    • 0343190798 scopus 로고
    • A structured phase transition for the anti-plane shear of an elastic circular tube
    • R.L. Fosdick and Y. Zhang, A structured phase transition for the anti-plane shear of an elastic circular tube. Quart. J. Mech. and Appl. Math. 48 (1995) 189-210.
    • (1995) Quart. J. Mech. and Appl. Math. , vol.48 , pp. 189-210
    • Fosdick, R.L.1    Zhang, Y.2
  • 14
    • 0000063775 scopus 로고
    • On the equilibrium of heterogeneous substances
    • Oct. May
    • J.W. Gibbs, On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy, III. 108-248, Oct. 1875-May, 1876 and 343-524, May, 1877-July, 1878.
    • (1875) Transactions of the Connecticut Academy , vol.3 , pp. 108-248
    • Gibbs, J.W.1
  • 15
    • 0000063775 scopus 로고
    • May, July
    • J.W. Gibbs, On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy, III. 108-248, Oct. 1875-May, 1876 and 343-524, May, 1877-July, 1878.
    • (1877) Transactions of the Connecticut Academy , pp. 343-524
  • 16
    • 0021853508 scopus 로고
    • On a theory of phase transitions with interfacial energy
    • M.E. Gurtin, On a theory of phase transitions with interfacial energy. Arch. Rational Mech. Anal. 87 (1985) 187-212.
    • (1985) Arch. Rational Mech. Anal. , vol.87 , pp. 187-212
    • Gurtin, M.E.1
  • 17
    • 2342540276 scopus 로고    scopus 로고
    • Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics
    • D.E. Mason, Phase transitions in nonlocal continuum mechanics., Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics, 1996.
    • (1996) Phase Transitions in Nonlocal Continuum Mechanics
    • Mason, D.E.1
  • 18
    • 34250109116 scopus 로고
    • Gradient theory of phase transitions and minimal interface criterion
    • L. Modica, Gradient theory of phase transitions and minimal interface criterion. Arch. Rational Mech. Anal. 98, No. 2 (1987) 123-142.
    • (1987) Arch. Rational Mech. Anal. , vol.98 , Issue.2 , pp. 123-142
    • Modica, L.1
  • 19
    • 0000254821 scopus 로고
    • Gradient theory of phase transitions with boundary contact energy
    • L. Modica, Gradient theory of phase transitions with boundary contact energy. Ann. Inst. Henri Poincaré 4 (1987) 487-512.
    • (1987) Ann. Inst. Henri Poincaré , vol.4 , pp. 487-512
    • Modica, L.1
  • 20
    • 0000390068 scopus 로고
    • Singular perturbations as a selection criterion for periodic minimizing sequences
    • S. Müller, Singular perturbations as a selection criterion for periodic minimizing sequences. Calculus of Variations 1 (1993) 169-204.
    • (1993) Calculus of Variations , vol.1 , pp. 169-204
    • Müller, S.1
  • 21
    • 84950350209 scopus 로고    scopus 로고
    • Some remarks on nonlocal interactions and hysteresis in phase transitions
    • R.C. Rogers, Some remarks on nonlocal interactions and hysteresis in phase transitions. Continuum Mech. Thermodyn. 8 (1996) 65-73.
    • (1996) Continuum Mech. Thermodyn. , vol.8 , pp. 65-73
    • Rogers, R.C.1
  • 22
    • 34250095380 scopus 로고
    • The effect of a singular perturbation on nonconvex variational problems
    • P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101 (1988) 209-260.
    • (1988) Arch. Rational Mech. Anal. , vol.101 , pp. 209-260
    • Sternberg, P.1
  • 23
    • 0002850821 scopus 로고
    • The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
    • In Dutch, Sect. 1
    • J.D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. (In Dutch), Verhandel. Konink. Akad. Weten. Amsterdam (Sect. 1) 1, No. 8 (1893).
    • (1893) Verhandel. Konink. Akad. Weten. Amsterdam , vol.1 , Issue.8
    • Van Der Waals, J.D.1
  • 24
    • 2342618041 scopus 로고
    • Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics
    • J.W. Walter, On a nonlocal model of fluid phases, Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics, 1985.
    • (1985) On a Nonlocal Model of Fluid Phases
    • Walter, J.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.