메뉴 건너뛰기




Volumn 162, Issue 4, 2002, Pages 287-325

A geometrical approach to the study of unbounded solutions of quasilinear parabolic equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036014324     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200188     Document Type: Article
Times cited : (46)

References (34)
  • 1
    • 0002237188 scopus 로고
    • Some recent results on mean curvature flow
    • ANGENENT, S.B.: Some recent results on mean curvature flow. RAM Res. Appl. Math. 30, 1-18 (1994).
    • (1994) RAM Res. Appl. Math. , vol.30 , pp. 1-18
    • Angenent, S.B.1
  • 4
    • 0003367760 scopus 로고
    • Remark on a flame propagation model
    • BARLES, G: Remark on a flame propagation model. Rapport INRIA 464 (1985).
    • (1985) Rapport INRIA , vol.464
    • Barles, G.1
  • 11
    • 0032386084 scopus 로고    scopus 로고
    • A new approach to front propagation problems: Theory and applications
    • BARLES, G. & SOUGANIDIS, P. E.: A new approach to front propagation problems: theory and applications. Arch. Rational Mech. Anal. 141, 237-296 (1998).
    • (1998) Arch. Rational Mech. Anal. , vol.141 , pp. 237-296
    • Barles, G.1    Souganidis, P.E.2
  • 13
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • CHEN, Y. G., GIGA, Y. & GOTO, S.: Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differential Geom. 33, 749-786 (1991)
    • (1991) J. Differential Geom. , vol.33 , pp. 749-786
    • Chen, Y.G.1    Giga, Y.2    Goto, S.3
  • 14
    • 0001588474 scopus 로고    scopus 로고
    • On quasilinear parabolic equations which admit global solutions for initial data with unrestricted growth
    • CHOU, K.-S. & KWONG, Y.-C.: On quasilinear parabolic equations which admit global solutions for initial data with unrestricted growth. Calc. Var. 12, 281-315 (2001).
    • (2001) Calc. Var. , vol.12 , pp. 281-315
    • Chou, K.-S.1    Kwong, Y.-C.2
  • 15
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • CRANDALL, M. G., ISHII, H. & LIONS, P.-L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27, 1-67 (1992).
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 16
    • 0001673425 scopus 로고
    • Interior estimates for hypersurfaces moving by mean curvature
    • ECKER, K. & HUISKEN, G.: Interior estimates for hypersurfaces moving by mean curvature. Invent. Math. 105, 547-569 (1991).
    • (1991) Invent. Math. , vol.105 , pp. 547-569
    • Ecker, K.1    Huisken, G.2
  • 17
    • 0030534516 scopus 로고    scopus 로고
    • A geometric interpretation of the heat equation with multivalued initial data
    • EVANS, L.C.: A geometric interpretation of the heat equation with multivalued initial data. SIAM J. Math. Anal. 27, 932-958 (1996).
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 932-958
    • Evans, L.C.1
  • 18
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature. I
    • EVANS, L. C. & SPRUCK, J.: Motion of level sets by mean curvature. I. J. Differential Geom. 33, 635-681 (1991).
    • (1991) J. Differential Geom. , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 19
    • 0000007598 scopus 로고
    • Motion of level sets by mean curvature. III
    • EVANS, L. C. & SPRUCK, J.: Motion of level sets by mean curvature. III. J. Geom. Anal. 2, 121-150 (1992).
    • (1992) J. Geom. Anal. , vol.2 , pp. 121-150
    • Evans, L.C.1    Spruck, J.2
  • 21
    • 0000357774 scopus 로고
    • Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains
    • GIGA, Y., GOTO, S., ISHII, H. & SATO, M.-H.: Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains. Indiana Univ. Math. J. 40, 443-470 (1991).
    • (1991) Indiana Univ. Math. J. , vol.40 , pp. 443-470
    • Giga, Y.1    Goto, S.2    Ishii, H.3    Sato, M.-H.4
  • 22
    • 22844453381 scopus 로고    scopus 로고
    • On semicontinuous solutions for general Hamilton-Jacobi equations
    • GIGA, Y. & SATO, M.-H.: On semicontinuous solutions for general Hamilton-Jacobi equations. Proc. Japan Acad. Ser. A Math. Sci. 75, 159-162 (1999).
    • (1999) Proc. Japan Acad. Ser. A Math. Sci. , vol.75 , pp. 159-162
    • Giga, Y.1    Sato, M.-H.2
  • 23
    • 84972537504 scopus 로고
    • Generalized motion of hypersurfaces whose growth speed depends superlinearly on the curvature tensor
    • GOTO, S.: Generalized motion of hypersurfaces whose growth speed depends superlinearly on the curvature tensor. Differential Integral Equations 7, 323-343 (1994).
    • (1994) Differential Integral Equations , vol.7 , pp. 323-343
    • Goto, S.1
  • 24
    • 0003295152 scopus 로고
    • Elliptic regularization and partial regularity for motion by mean curvature
    • ILMANEN, T.: Elliptic regularization and partial regularity for motion by mean curvature. Mem. Amer. Math. Soc. 108(520) (1994).
    • (1994) Mem. Amer. Math. Soc. , vol.108 , Issue.520
    • Ilmanen, T.1
  • 26
    • 84972566521 scopus 로고
    • Perron's method for Hamilton-Jacobi equations
    • ISHII, H.: Perron's method for Hamilton-Jacobi equations. Duke Math. J. 55, 369-384 (1987).
    • (1987) Duke Math. J. , vol.55 , pp. 369-384
    • Ishii, H.1
  • 27
    • 0013035240 scopus 로고    scopus 로고
    • Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces
    • ISHII, H.: Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces. Adv. Differential Equations 1, 51-72 (1996).
    • (1996) Adv. Differential Equations , vol.1 , pp. 51-72
    • Ishii, H.1
  • 28
    • 84972546686 scopus 로고
    • Generalized motion of non compact hypersurfaces with velocity having arbitrary growth on the curvature tensor
    • ISHII, H. & SOUGANIDIS, P.E.: Generalized motion of non compact hypersurfaces with velocity having arbitrary growth on the curvature tensor. Tôhuko Math. J. 47, 227-250 (1995).
    • (1995) Tôhuko Math. J. , vol.47 , pp. 227-250
    • Ishii, H.1    Souganidis, P.E.2
  • 29
    • 0001156676 scopus 로고
    • Linear and quasilinear equations of parabolic type
    • American Mathematical Society, Providence, R.I., Translated from the Russian by S. Smith.
    • LADYZENSKAJA, O. A., SOLONNIKOV, V. A. & URAL'CEVA, N. N.: Linear and quasilinear equations of parabolic type. American Mathematical Society, Providence, R.I., 1967. Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23.
    • (1967) Translations of Mathematical Monographs , vol.23
    • Ladyzenskaja, O.A.1    Solonnikov, V.A.2    Ural'ceva, N.N.3
  • 30
    • 84972520473 scopus 로고
    • Singular degenerate parabolic equations with applications to geometric evolutions
    • OHNUMA, M. & SATO, K.: Singular degenerate parabolic equations with applications to geometric evolutions. Differential Integral Equations6, 1265-1280 (1993).
    • (1993) Differential Integral Equations , vol.6 , pp. 1265-1280
    • Ohnuma, M.1    Sato, K.2
  • 31
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • OSHER, S. & SETHIAN, J.: Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Physics 79, 12-49 (1988).
    • (1988) J. Comp. Physics , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.2
  • 32
    • 0000935065 scopus 로고
    • Motion of a set by the curvature of its boundary
    • SONER, H. M.: Motion of a set by the curvature of its boundary. J. Differential Equations 101, 313-372 (1993).
    • (1993) J. Differential Equations , vol.101 , pp. 313-372
    • Soner, H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.