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Volumn 3, Issue 1, 1998, Pages 85-110

A convolution model for interfacial motion: The generation and propagation of internal layers in higher space dimensions

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EID: 0002995185     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (61)

References (31)
  • 1
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusion arising in population genetics
    • D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Advances in Math. 30 (1978), 33-76.
    • (1978) Advances in Math. , vol.30 , pp. 33-76
    • Aronson, D.G.1    Weinberger, H.F.2
  • 2
    • 84894555273 scopus 로고    scopus 로고
    • A new approach to front propagation problems: theory and applications
    • preprint
    • G. Barles and P.E. Souganidis, A new approach to front propagation problems: theory and applications, preprint.
    • Barles, G.1    Souganidis, P.E.2
  • 4
    • 0031282920 scopus 로고    scopus 로고
    • Traveling waves in a convolution model for phase transitions
    • Peter W. Bates, Paul C. Fife, Xiaofeng Ren, and Xuefeng Wang, Traveling waves in a convolution model for phase transitions, Arch. Rat. Mech. Anal., 138 (1997), 105-136.
    • (1997) Arch. Rat. Mech. Anal. , vol.138 , pp. 105-136
    • Bates, P.W.1    Fife, P.C.2    Ren, X.3    Wang, X.4
  • 5
    • 0001314971 scopus 로고
    • Dynamics of layered interfaces arising from phase boundaries
    • G. Caginalp and P.C. Fife, Dynamics of layered interfaces arising from phase boundaries, SIAM J. Appl. Math., 48 (1988), 506-518.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 506-518
    • Caginalp, G.1    Fife, P.C.2
  • 6
    • 6244279498 scopus 로고
    • Theory of crystal growth and interface motion in crystalline materials
    • J.W. Cahn, Theory of crystal growth and interface motion in crystalline materials, Acta Metallurgica, 8 (1960), 554-562.
    • (1960) Acta Metallurgica , vol.8 , pp. 554-562
    • Cahn, J.W.1
  • 7
    • 0001924513 scopus 로고
    • A microscopic theory for domain wall motion and its experimental verification in Fe-Al alloy domain growth kinetics
    • J.W. Cahn and S.M. Allen, A microscopic theory for domain wall motion and its experimental verification in Fe-Al alloy domain growth kinetics, J. de Physique 38 Colloque C7 (1977), 51-54.
    • (1977) J. de Physique 38 Colloque , vol.C7 , pp. 51-54
    • Cahn, J.W.1    Allen, S.M.2
  • 8
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • J.W. Cahn and S.M. Allen, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta. Met. 27 (1979), 1085-1095.
    • (1979) Acta. Met. , vol.27 , pp. 1085-1095
    • Cahn, J.W.1    Allen, S.M.2
  • 9
    • 0001249829 scopus 로고
    • Generation and propagation of interface in reaction-diffusion equations
    • Xinfu Chen, Generation and propagation of interface in reaction-diffusion equations, J. Diff. Equations, 96 (1992), 116-141.
    • (1992) J. Diff. Equations , vol.96 , pp. 116-141
    • Chen, X.1
  • 10
    • 84990617538 scopus 로고
    • Phase transitions and generalized motion by mean curvature
    • L.C. Evans, H.M. Soner, and P.E. Souganidis, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math., 45 (1992), 1097-1123.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 1097-1123
    • Evans, L.C.1    Soner, H.M.2    Souganidis, P.E.3
  • 11
    • 0002910353 scopus 로고
    • Long time behavior of solutions of bistable nonlinear diffusion equations
    • P.C. Fife, Long time behavior of solutions of bistable nonlinear diffusion equations, Arch. Rat. Mech. Anal., 70 (1979), 31-46.
    • (1979) Arch. Rat. Mech. Anal. , vol.70 , pp. 31-46
    • Fife, P.C.1
  • 12
    • 84983705485 scopus 로고
    • Dynamics of Internal Layers and Diffusive Interfaces
    • CBMS-NSF Regional Conference Series in Applied Mathematics No.53 (19), Soc. Ind. Appl. Math, Philadelphia
    • P.C. Fife, Dynamics of Internal Layers and Diffusive Interfaces, CBMS-NSF Regional Conference Series in Applied Mathematics No.53 (19), Soc. Ind. Appl. Math, Philadelphia (1988).
    • (1988)
    • Fife, P.C.1
  • 13
    • 84894546257 scopus 로고
    • Barrett Lecture Notes
    • Univ. of Tennessee
    • P.C. Fife, "Barrett Lecture Notes," Univ. of Tennessee, 1991.
    • (1991)
    • Fife, P.C.1
  • 14
    • 0039215869 scopus 로고
    • Models for phase separation and their mathematics
    • in "Nonlinear Partial Differential Equations with Applications to Patterns, Waves, and Interfaces" (M. Mimura and T. Nishida, eds.), Proc. Conf. on Nonlinear Partial Differential Equations, Kyoto (unpublished).
    • P.C. Fife, Models for phase separation and their mathematics, in "Nonlinear Partial Differential Equations with Applications to Patterns, Waves, and Interfaces" (M. Mimura and T. Nishida, eds.), pp. 183-212, Proc. Conf. on Nonlinear Partial Differential Equations, Kyoto (1992) (unpublished).
    • (1992) , pp. 183-212
    • Fife, P.C.1
  • 15
    • 0039088719 scopus 로고
    • The generation and propagation of internal layers
    • P.C. Fife and L. Hsiao, The generation and propagation of internal layers, Nonlinear Anal., 70 (1988), 31-46.
    • (1988) Nonlinear Anal. , vol.70 , pp. 31-46
    • Fife, P.C.1    Hsiao, L.2
  • 16
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling front solutions
    • Also announcement in "Bull. Amer. Math. Soc., 81 (1975), 1075-1078.
    • P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal., 65 (1977), 335-361. Also announcement in "Bull. Amer. Math. Soc., 81 (1975), 1075-1078.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 17
    • 0019661804 scopus 로고
    • A phase plane discussion of convergence to travelling fronts for nonlinear diffusion
    • P.C. Fife and J.B. McLeod, A phase plane discussion of convergence to travelling fronts for nonlinear diffusion, Arch. Rat. Mech. Anal., 75 (1981), 281-314.
    • (1981) Arch. Rat. Mech. Anal. , vol.75 , pp. 281-314
    • Fife, P.C.1    McLeod, J.B.2
  • 18
    • 0003016830 scopus 로고
    • Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter
    • P.C. Fife and O. Penrose, Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter, Electronic J. Differential Eqns. (1995), 1-49.
    • (1995) Electronic J. Differential Eqns. , pp. 1-49
    • Fife, P.C.1    Penrose, O.2
  • 19
    • 0039565152 scopus 로고
    • Bistable reaction-diffusion equations and excitable media
    • J. Gärtner, Bistable reaction-diffusion equations and excitable media, Math. Nachr., 112 (1983), 125-152.
    • (1983) Math. Nachr. , vol.112 , pp. 125-152
    • Gärtner, J.1
  • 20
    • 21844481773 scopus 로고
    • Travelling fronts in non local evolution equations
    • A. de Masi, T. Gobron, and E. Presutti, Travelling fronts in non local evolution equations, Arch. Rat. Mech. Anal., 132 (1995), 143-205.
    • (1995) Arch. Rat. Mech. Anal. , vol.132 , pp. 143-205
    • de Masi, A.1    Gobron, T.2    Presutti, E.3
  • 21
    • 21344476649 scopus 로고
    • Motion by curvature by scaling nonlocal evolution equations
    • A. de Masi, E. Orlandi, E. Presutti, and L. Triolo, Motion by curvature by scaling nonlocal evolution equations, J. Stat. Physics, 73 (1993), 543-570.
    • (1993) J. Stat. Physics , vol.73 , pp. 543-570
    • de Masi, A.1    Orlandi, E.2    Presutti, E.3    Triolo, L.4
  • 23
    • 0003354543 scopus 로고
    • Uniqueness of the instanton profile and global stability in non local evolution equations
    • A. de Masi, E. Orlandi, E. Presutti, and L. Triolo, Uniqueness of the instanton profile and global stability in non local evolution equations, Rend. Math., 14 (1994), 693-723.
    • (1994) Rend. Math. , vol.14 , pp. 693-723
    • de Masi, A.1    Orlandi, E.2    Presutti, E.3    Triolo, L.4
  • 24
    • 0001318159 scopus 로고
    • Evolution geometrique d'interfaces
    • P. de Mottoni and M. Schatzman, Evolution geometrique d'interfaces, C. R. Acad. Paris, 309 (1989), 453-458.
    • (1989) C. R. Acad. Paris , vol.309 , pp. 453-458
    • de Mottoni, P.1    Schatzman, M.2
  • 25
    • 0000161576 scopus 로고
    • Geometrical evolution of developed interfaces
    • P. de Mottoni and M. Schatzman, Geometrical evolution of developed interfaces, Trans. Amer. Math. Soc., 347 (1995), 1533-1544.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1533-1544
    • de Mottoni, P.1    Schatzman, M.2
  • 26
    • 84972434011 scopus 로고
    • Development of interfaces in N-dimensional space
    • P. de Mottoni and M. Schatzman, Development of interfaces in N-dimensional space, Proc. Roy. Soc. Edinburgh, 116A (1990), 207-220.
    • (1990) Proc. Roy. Soc. Edinburgh , vol.116 A , pp. 207-220
    • de Mottoni, P.1    Schatzman, M.2
  • 27
    • 21744444381 scopus 로고    scopus 로고
    • Traveling fronts in nonlocal models for phase separation in external field
    • E. Orlandi and L. Triolo, Traveling fronts in nonlocal models for phase separation in external field, Proceeding of the Royal Society of Edinburgh, 127A (1997), 823-835.
    • (1997) Proceeding of the Royal Society of Edinburgh , vol.127 A , pp. 823-835
    • Orlandi, E.1    Triolo, L.2
  • 28
  • 29
    • 0038496301 scopus 로고
    • Reaction-diffusion processes and evolution to harmonic maps
    • J. Rubinstein, P. Sternberg, and J.B. Keller, Reaction-diffusion processes and evolution to harmonic maps, SIAM J. Appl. Math., 49 (1989), 1722-1733.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1722-1733
    • Rubinstein, J.1    Sternberg, P.2    Keller, J.B.3
  • 30
    • 84894544189 scopus 로고    scopus 로고
    • Ginzburg-Landau equation and motion by mean curvature
    • I: convergence; II: Development of the initial interface, J. Geom. Anal, in press
    • H.M. Soner, Ginzburg-Landau equation and motion by mean curvature, I: convergence; II: Development of the initial interface, J. Geom. Anal, in press.
    • Soner, H.M.1
  • 31
    • 0001940781 scopus 로고    scopus 로고
    • Front propagation: Theory and applications
    • CIME Course on Viscosity Solutions, Lect. Notes in Mathematics, Springer-Verlag, in press
    • P.E. Souganidis, "Front propagation: Theory and applications," CIME Course on Viscosity Solutions, Lect. Notes in Mathematics, Springer-Verlag, in press.
    • Souganidis, P.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.