메뉴 건너뛰기




Volumn 38, Issue 5, 2006, Pages 1694-1713

Global existence of classical solutions for a haptotaxis model

Author keywords

Classical solutions; Diffusion; Global existence; Haptotaxis; Uniqueness

Indexed keywords

DIFFUSION; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; SYSTEMS ANALYSIS; TUMORS;

EID: 34548693955     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/060655122     Document Type: Article
Times cited : (130)

References (24)
  • 1
    • 51249186677 scopus 로고
    • Dual semigroups and second order linear elliptic boundary value problems
    • H. AMANN. Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math., 45 (1983), pp. 225-254.
    • (1983) Israel J. Math , vol.45 , pp. 225-254
    • AMANN, H.1
  • 2
    • 0040945506 scopus 로고    scopus 로고
    • Multiplication in Sobolev and Besov spaces, in Nonlinear Analysis
    • Norm
    • H. AMANN, Multiplication in Sobolev and Besov spaces, in Nonlinear Analysis. A Tribute in Honour of Giovanni Prodi, Quaderni, Scuola Norm. Sup., 1991, pp. 27-57.
    • A Tribute in Honour of Giovanni Prodi, Quaderni, Scuola , Issue.SUP.and 1991 , pp. 27-57
    • AMANN, H.1
  • 4
    • 27144523168 scopus 로고    scopus 로고
    • Local and global strong solutions to continuous coagulationfragmentation equations with diffusion
    • H. AMANN AND CH. WALKER, Local and global strong solutions to continuous coagulationfragmentation equations with diffusion, J. Differential Equations, 218 (2004), pp. 1-28.
    • (2004) J. Differential Equations , vol.218 , pp. 1-28
    • AMANN, H.1    WALKER, C.2
  • 5
    • 25144494216 scopus 로고    scopus 로고
    • A. R. A. ANDERSON, A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion, Math. Med. Biol. IMA J., 22 (2005), pp. 163-186.
    • A. R. A. ANDERSON, A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion, Math. Med. Biol. IMA J., 22 (2005), pp. 163-186.
  • 6
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumor-induced angiogenesis
    • A. R. A. ANDERSON AND M. CHAPLAIN, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Biol., 60 (1998), pp. 857-900.
    • (1998) Bull. Math. Biol , vol.60 , pp. 857-900
    • ANDERSON, A.R.A.1    CHAPLAIN, M.2
  • 7
    • 33847793521 scopus 로고    scopus 로고
    • Computational methods and results for structured multiscale models of tumor invasion
    • B. AYATI, A. R. A. ANDERSON, AND G. F. WEBB, Computational methods and results for structured multiscale models of tumor invasion, Multiscale Model. Simul., 5 (2006), pp. 120.
    • (2006) Multiscale Model. Simul , vol.5 , pp. 120
    • AYATI, B.1    ANDERSON, A.R.A.2    WEBB, G.F.3
  • 8
    • 0013850974 scopus 로고
    • Principles of cell motility: The direction of cell movement and cancer invasion
    • S. B. CARTER, Principles of cell motility: The direction of cell movement and cancer invasion, Nature, 208 (1965), pp. 1183-1187.
    • (1965) Nature , vol.208 , pp. 1183-1187
    • CARTER, S.B.1
  • 9
    • 0014212671 scopus 로고
    • Haptotaxis and the mechanism of cell motility
    • S. B. CARTER, Haptotaxis and the mechanism of cell motility, Nature, 213 (1967), pp. 256-260.
    • (1967) Nature , vol.213 , pp. 256-260
    • CARTER, S.B.1
  • 11
    • 26844499863 scopus 로고    scopus 로고
    • Global solutions of some Chemotaxis and angiogenesis systems in high space dimensions
    • L. CORRIAS, B. PERTHAME, AND H. ZAAG, Global solutions of some Chemotaxis and angiogenesis systems in high space dimensions, Milan J. Math., 72 (2004), pp. 159-186.
    • (2004) Milan J. Math , vol.72 , pp. 159-186
    • CORRIAS, L.1    PERTHAME, B.2    ZAAG, H.3
  • 12
    • 0036433997 scopus 로고    scopus 로고
    • Mathematical analysis of a model for the initiation of angiogenesis
    • M. A. FONTELOS, A. FRIEDMAN, AND B. HU, Mathematical analysis of a model for the initiation of angiogenesis, SIAM J. Math. Anal., 33 (2002), pp. 1330-1355.
    • (2002) SIAM J. Math. Anal , vol.33 , pp. 1330-1355
    • FONTELOS, M.A.1    FRIEDMAN, A.2    HU, B.3
  • 13
    • 0036700354 scopus 로고    scopus 로고
    • Stability of solutions of Chemotaxis equations in reinforced random walks
    • A. FRIEDMAN AND J. I. TELLO, Stability of solutions of Chemotaxis equations in reinforced random walks, J. Math. Anal. Appl., 272 (2002), pp. 138-163.
    • (2002) J. Math. Anal. Appl , vol.272 , pp. 138-163
    • FRIEDMAN, A.1    TELLO, J.I.2
  • 14
    • 13644283506 scopus 로고    scopus 로고
    • Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones
    • F. R. GUARGUAGLINI AND R. NATALINI, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones, Nonlinear Anal. Real World Appl., 6 (2005), pp. 477-494.
    • (2005) Nonlinear Anal. Real World Appl , vol.6 , pp. 477-494
    • GUARGUAGLINI, F.R.1    NATALINI, R.2
  • 15
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin, New York
    • D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer, Berlin, New York, 1981.
    • (1981) Lecture Notes in Math , vol.840
    • HENRY, D.1
  • 16
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in Chemotaxis and its consequences I
    • D. HORSTMANN, From 1970 until present: The Keller-Segel model in Chemotaxis and its consequences I, Jahresber. Deutsch. Math.-Verein., 105 (2003), pp. 103-165.
    • (2003) Jahresber. Deutsch. Math.-Verein , vol.105 , pp. 103-165
    • HORSTMANN, D.1
  • 17
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • H. A. LEVINE AND B. D. SLEEMAN, A system of reaction diffusion equations arising in the theory of reinforced random walks, SIAM J. Appl. Math., 57 (1997), pp. 683-730.
    • (1997) SIAM J. Appl. Math , vol.57 , pp. 683-730
    • LEVINE, H.A.1    SLEEMAN, B.D.2
  • 18
    • 0141644434 scopus 로고    scopus 로고
    • Finite dimensional attractor for one-dimensional Keller-Segel equations
    • K. OSAKI AND A. YAGI, Finite dimensional attractor for one-dimensional Keller-Segel equations, Funkcial. Ekvac., 44 (2001), pp. 441-469.
    • (2001) Funkcial. Ekvac , vol.44 , pp. 441-469
    • OSAKI, K.1    YAGI, A.2
  • 19
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks
    • H. G. OTHMER AND A. STEVENS, Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks, SIAM J. Appl. Math., 57 (1997), pp. 1044-1081.
    • (1997) SIAM J. Appl. Math , vol.57 , pp. 1044-1081
    • OTHMER, H.G.1    STEVENS, A.2
  • 20
    • 0000714743 scopus 로고
    • On a system of nonlinear strongly coupled partial differential equations arising in biology
    • Ordinary and Partial Differential Equations, W. N. Everitt and B. D. Sleeman, eds, Springer-Verlag, New York
    • M. RASCLE, On a system of nonlinear strongly coupled partial differential equations arising in biology, in Ordinary and Partial Differential Equations, W. N. Everitt and B. D. Sleeman, eds., Lecture Notes in Math. 846, Springer-Verlag, New York, 1980, pp. 290-298.
    • (1980) Lecture Notes in Math , vol.846 , pp. 290-298
    • RASCLE, M.1
  • 21
    • 0029192972 scopus 로고
    • Finite time blow-up in some models of Chemotaxis
    • M. RASCLE AND C. ZITI, Finite time blow-up in some models of Chemotaxis, J. Math. Biol., 33 (1995), pp. 388-414.
    • (1995) J. Math. Biol , vol.33 , pp. 388-414
    • RASCLE, M.1    ZITI, C.2
  • 22
    • 0003250029 scopus 로고
    • Global Solutions of Reaction-Diffusion Systems
    • Springer, Berlin, Heidelberg, New York, Tokyo
    • F. ROTHE, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Math. 1072, Springer, Berlin, Heidelberg, New York, Tokyo, 1984.
    • (1984) Lecture Notes in Math , vol.1072
    • ROTHE, F.1
  • 23
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of Chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
    • A. STEVENS, The derivation of Chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems, SIAM J. Appl. Math., 61 (2000), pp. 183-212.
    • (2000) SIAM J. Appl. Math , vol.61 , pp. 183-212
    • STEVENS, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.