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Volumn 72, Issue 1, 2010, Pages 77-98

Global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology

Author keywords

Asymptotic behavior; Classical solutions; Global existence; Parabolic degenerate system; Steady state

Indexed keywords

ASYMPTOTIC BEHAVIORS; BIOLOGICAL PROCESS; BOUNDED DOMAIN; CLASSICAL SOLUTIONS; COUPLED SYSTEMS; EUCLIDEAN SPACES; GLOBAL EXISTENCE; GLOBAL EXISTENCE AND UNIQUENESS; GLOBAL SOLUTIONS; STEADY STATE;

EID: 71749113781     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.06.083     Document Type: Article
Times cited : (20)

References (29)
  • 1
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as instability
    • Keller E.F., and Segel L.A. Initiation of slime mold aggregation viewed as instability. J. Theoret. Biol. 26 (1970) 399-415
    • (1970) J. Theoret. Biol. , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 2
    • 0016679509 scopus 로고
    • Necessary and sufficient conditions for chemotactic bands
    • Keller E.F., and Odell G.M. Necessary and sufficient conditions for chemotactic bands. Math. Biosci. 27 (1975) 309-317
    • (1975) Math. Biosci. , vol.27 , pp. 309-317
    • Keller, E.F.1    Odell, G.M.2
  • 3
    • 0017184096 scopus 로고
    • Traveling bands of chemotactic bacteria revisited
    • Keller E.F., and Odell G.M. Traveling bands of chemotactic bacteria revisited. J. Theoret. Biol. 56 (1976) 243-247
    • (1976) J. Theoret. Biol. , vol.56 , pp. 243-247
    • Keller, E.F.1    Odell, G.M.2
  • 4
    • 0015010990 scopus 로고
    • Traveling bands of chemotactic bacteria: A theoretical analysis
    • Keller E.F., and Segel L.A. Traveling bands of chemotactic bacteria: A theoretical analysis. J. Theoret. Biol. 30 (1971) 235-248
    • (1971) J. Theoret. Biol. , vol.30 , pp. 235-248
    • Keller, E.F.1    Segel, L.A.2
  • 5
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I
    • Horstmann D. From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I. Jahresber. Deutsch. Math.-Verein. 105 (2003) 103-165
    • (2003) Jahresber. Deutsch. Math.-Verein. , vol.105 , pp. 103-165
    • Horstmann, D.1
  • 6
    • 13844288282 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences II
    • Horstmann D. From 1970 until present: The Keller-Segel model in chemotaxis and its consequences II. Jahresber. Deutsch. Math.-Verein. 106 (2004) 51-69
    • (2004) Jahresber. Deutsch. Math.-Verein. , vol.106 , pp. 51-69
    • Horstmann, D.1
  • 7
    • 25144494216 scopus 로고    scopus 로고
    • A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion
    • Anderson A.R.A. A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion. IMA J. Math. Med. Biol. 22 (2005) 163-186
    • (2005) IMA J. Math. Med. Biol. , vol.22 , pp. 163-186
    • Anderson, A.R.A.1
  • 8
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumour-induced angiogenesis
    • Anderson A.R.A., and Chaplain M. Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Biol. 60 (1998) 857-900
    • (1998) Bull. Math. Biol. , vol.60 , pp. 857-900
    • Anderson, A.R.A.1    Chaplain, M.2
  • 9
    • 2542459083 scopus 로고    scopus 로고
    • Mathematical modelling of tissue invasion
    • Preziosi L. (Ed), Chapman Hall/CRC (Chapter 10)
    • Chaplain M. Mathematical modelling of tissue invasion. In: Preziosi L. (Ed). Cancer Modelling and Simulation (2003), Chapman Hall/CRC 269-297 (Chapter 10)
    • (2003) Cancer Modelling and Simulation , pp. 269-297
    • Chaplain, M.1
  • 10
    • 16644400591 scopus 로고    scopus 로고
    • Mathematical modelling of tumour induced angiogenesis
    • Mantzaris N.V., Webb S., and Othmer H.G. Mathematical modelling of tumour induced angiogenesis. J. Math. Biol. 49 (2004) 111-187
    • (2004) J. Math. Biol. , vol.49 , pp. 111-187
    • Mantzaris, N.V.1    Webb, S.2    Othmer, H.G.3
  • 11
    • 0039440566 scopus 로고    scopus 로고
    • A two parameter family of travelling waves with a singular barrier arising from the modelling of matrix mediated malignant invasion
    • Perumpanani A.J., Sherratt J.A., Norbury J., and Byrne H.M. A two parameter family of travelling waves with a singular barrier arising from the modelling of matrix mediated malignant invasion. Physica D. 126 (1999) 145-159
    • (1999) Physica D. , vol.126 , pp. 145-159
    • Perumpanani, A.J.1    Sherratt, J.A.2    Norbury, J.3    Byrne, H.M.4
  • 12
    • 41149151126 scopus 로고    scopus 로고
    • Global well-posedness of a haptotaxis model including age and spatial structure
    • Walker C. Global well-posedness of a haptotaxis model including age and spatial structure. Differential Integral Equations 20 (2007) 1053-1074
    • (2007) Differential Integral Equations , vol.20 , pp. 1053-1074
    • Walker, C.1
  • 13
    • 34548693955 scopus 로고    scopus 로고
    • Global existence of classical solutions for a haptotaxis model
    • Walker C., and Webb G.F. Global existence of classical solutions for a haptotaxis model. SIAM J. Math. Anal. 38 (2007) 1694-1713
    • (2007) SIAM J. Math. Anal. , vol.38 , pp. 1694-1713
    • Walker, C.1    Webb, G.F.2
  • 14
    • 0000714743 scopus 로고
    • On a system of non linear strongly coupled partial differential equations arising in Biology
    • Everitt, and Sleeman (Eds), Springer-Verlag, New-York
    • Rascle M. On a system of non linear strongly coupled partial differential equations arising in Biology. In: Everitt, and Sleeman (Eds). Lectures Notes in Math. vol. 846 (1980), Springer-Verlag, New-York 290-298
    • (1980) Lectures Notes in Math. , vol.846 , pp. 290-298
    • Rascle, M.1
  • 15
    • 0000715275 scopus 로고
    • Sur un équation intégro-différentielle non linéaire issue de la biologie
    • Rascle M. Sur un équation intégro-différentielle non linéaire issue de la biologie. J. Differential Equations 32 (1979) 420-453
    • (1979) J. Differential Equations , vol.32 , pp. 420-453
    • Rascle, M.1
  • 16
    • 13644283506 scopus 로고    scopus 로고
    • Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones
    • Guarguaglini F.R., and Natalini R. Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones. Nonlinear Anal. RWA 6 (2005) 477-494
    • (2005) Nonlinear Anal. RWA , vol.6 , pp. 477-494
    • Guarguaglini, F.R.1    Natalini, R.2
  • 18
    • 26844499863 scopus 로고    scopus 로고
    • Global solutions in some chemotaxis and angiogenesis systems in high space dimensions
    • Corrias L., Perthame B., and Zaag H. Global solutions in some chemotaxis and angiogenesis systems in high space dimensions. Milan J. Math. 72 (2004) 1-28
    • (2004) Milan J. Math. , vol.72 , pp. 1-28
    • Corrias, L.1    Perthame, B.2    Zaag, H.3
  • 20
    • 34248170756 scopus 로고    scopus 로고
    • Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology
    • Guarguaglini F.R., and Natalini R. Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology. Commun. Pure Appl. Anal. 6 (2007) 287-309
    • (2007) Commun. Pure Appl. Anal. , vol.6 , pp. 287-309
    • Guarguaglini, F.R.1    Natalini, R.2
  • 21
    • 6444228071 scopus 로고    scopus 로고
    • Mathematical analysis and stability of a chemotaxis model with logistic term
    • Tello J.I. Mathematical analysis and stability of a chemotaxis model with logistic term. Math. Methods Appl. Sci. 27 (2004) 1865-1880
    • (2004) Math. Methods Appl. Sci. , vol.27 , pp. 1865-1880
    • Tello, J.I.1
  • 22
    • 0036433997 scopus 로고    scopus 로고
    • Mathematical analysis of a model for the initiation of angiogenesis
    • Fontelos M.A., Friedman A., and Hu B. Mathematical analysis of a model for the initiation of angiogenesis. SIAM J. Math. Anal. 33 (2002) 1330-1355
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1330-1355
    • Fontelos, M.A.1    Friedman, A.2    Hu, B.3
  • 23
    • 0036700354 scopus 로고    scopus 로고
    • Stability of solutions of chemotaxis equations in reinforced random walks
    • Friedman A., and Tello J.I. Stability of solutions of chemotaxis equations in reinforced random walks. J. Math. Anal. Appl. 272 (2002) 138-163
    • (2002) J. Math. Anal. Appl. , vol.272 , pp. 138-163
    • Friedman, A.1    Tello, J.I.2
  • 24
    • 0032445844 scopus 로고    scopus 로고
    • Global behaviour of a reaction-diffusion system modelling chemotaxis
    • Gajewski H., and Zacharias K. Global behaviour of a reaction-diffusion system modelling chemotaxis. Math. Nachr. 195 (1998) 77-114
    • (1998) Math. Nachr. , vol.195 , pp. 77-114
    • Gajewski, H.1    Zacharias, K.2
  • 25
    • 0005525774 scopus 로고    scopus 로고
    • p estimates for a class of reaction-diffusion systems
    • p estimates for a class of reaction-diffusion systems. Colloq. Math. 87 (2001) 113-127
    • (2001) Colloq. Math. , vol.87 , pp. 113-127
    • Horstmann, D.1
  • 27
    • 33746512204 scopus 로고    scopus 로고
    • A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
    • Reyes G., and Vázquez J.L. A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media. J. Eur. Math. Soc. 8 (2006) 531-554
    • (2006) J. Eur. Math. Soc. , vol.8 , pp. 531-554
    • Reyes, G.1    Vázquez, J.L.2
  • 28
    • 0040232585 scopus 로고
    • On the time-dependent drift-diffusion model for semiconductors
    • Fang W., and Ito K. On the time-dependent drift-diffusion model for semiconductors. J. Differential Equations 117 (1995) 245-280
    • (1995) J. Differential Equations , vol.117 , pp. 245-280
    • Fang, W.1    Ito, K.2
  • 29


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.