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Volumn 367, Issue 2, 2010, Pages 612-624

A density-dependent chemotaxis-haptotaxis system modeling cancer invasion

Author keywords

Cancer invasion model; Chemotaxis; Global existence; Haptotaxis; Logistic source

Indexed keywords


EID: 77949560849     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2010.02.015     Document Type: Article
Times cited : (26)

References (45)
  • 2
  • 3
    • 44349107599 scopus 로고    scopus 로고
    • On the foundations of cancer modelling: selected topics, speculations, and perspectives
    • Bellomo N., Li N.K., and Maini P.K. On the foundations of cancer modelling: selected topics, speculations, and perspectives. Math. Models Methods Appl. Sci. 18 (2008) 593-646
    • (2008) Math. Models Methods Appl. Sci. , vol.18 , pp. 593-646
    • Bellomo, N.1    Li, N.K.2    Maini, P.K.3
  • 4
    • 33645680010 scopus 로고    scopus 로고
    • Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions
    • 32 pp. (electronic)
    • Blanchet A., Dolbeault J., and Perthame B. Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions. Electron. J. Differential Equations 44 (2006) 32 pp. (electronic)
    • (2006) Electron. J. Differential Equations , vol.44
    • Blanchet, A.1    Dolbeault, J.2    Perthame, B.3
  • 5
    • 33746377577 scopus 로고    scopus 로고
    • Volume effects in the Keller-Segel model: energy estimates preventing blow-up
    • Calvez V., and Carrillo J.A. Volume effects in the Keller-Segel model: energy estimates preventing blow-up. J. Math. Pures Appl. (9) 86 (2006) 155-175
    • (2006) J. Math. Pures Appl. (9) , vol.86 , pp. 155-175
    • Calvez, V.1    Carrillo, J.A.2
  • 6
    • 2542459083 scopus 로고    scopus 로고
    • Mathematical modelling of tissue invasion
    • Preziosi L. (Ed), Chapman & Hall/CRT
    • Chaplain M.A.J., and Anderson A.R.A. Mathematical modelling of tissue invasion. In: Preziosi L. (Ed). Cancer Modelling and Simulation (2003), Chapman & Hall/CRT 267-297
    • (2003) Cancer Modelling and Simulation , pp. 267-297
    • Chaplain, M.A.J.1    Anderson, A.R.A.2
  • 7
    • 85182867322 scopus 로고    scopus 로고
    • Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
    • Chaplain M.A.J., and Lolas G. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Netw. Heterog. Media 1 (2006) 399-439
    • (2006) Netw. Heterog. Media , vol.1 , pp. 399-439
    • Chaplain, M.A.J.1    Lolas, G.2
  • 8
    • 61649113706 scopus 로고    scopus 로고
    • Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system
    • Cieślak T., and Laurençot P. Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system. C. R. Acad. Sci. Paris Sér. I 347 (2009) 237-242
    • (2009) C. R. Acad. Sci. Paris Sér. I , vol.347 , pp. 237-242
    • Cieślak, T.1    Laurençot, P.2
  • 9
    • 43049112453 scopus 로고    scopus 로고
    • Finite-time blow-up in a quasilinear system of chemotaxis
    • Cieślak T., and Winkler M. Finite-time blow-up in a quasilinear system of chemotaxis. Nonlinearity 21 (2008) 1057-1076
    • (2008) Nonlinearity , vol.21 , pp. 1057-1076
    • Cieślak, T.1    Winkler, M.2
  • 10
    • 26844499863 scopus 로고    scopus 로고
    • Global solutions of some chemotaxis and angiogenesis systems in high space dimensions
    • Corrias L., Perthame B., and Zaag H. Global solutions of 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
  • 11
    • 71749091811 scopus 로고    scopus 로고
    • An angiogenesis model with nonlinear chemotactic response and flux at the tumor boundary
    • Delgado M., Gayte I., Morales-Rodrigo C., and Suárez A. An angiogenesis model with nonlinear chemotactic response and flux at the tumor boundary. Nonlinear Anal. 72 (2010) 330-347
    • (2010) Nonlinear Anal. , vol.72 , pp. 330-347
    • Delgado, M.1    Gayte, I.2    Morales-Rodrigo, C.3    Suárez, A.4
  • 12
    • 0029751950 scopus 로고    scopus 로고
    • A reaction-diffusion model of cancer invasion
    • Gatenby R.A., and Gawlinski E.T. A reaction-diffusion model of cancer invasion. Cancer Res. 56 (1996) 5745-5753
    • (1996) Cancer Res. , vol.56 , pp. 5745-5753
    • Gatenby, R.A.1    Gawlinski, E.T.2
  • 13
    • 38649104788 scopus 로고    scopus 로고
    • Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion
    • Gerisch A., and Chaplain M.A.J. Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion. J. Theoret. Biol. 250 (2008) 684-704
    • (2008) J. Theoret. Biol. , vol.250 , pp. 684-704
    • Gerisch, A.1    Chaplain, M.A.J.2
  • 14
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin
    • Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. vol. 840 (1981), Springer, Berlin
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 16
    • 0001404830 scopus 로고    scopus 로고
    • Global existence for a parabolic chemotaxis model with prevention of overcrowding
    • Hillen T., and Painter K.J. Global existence for a parabolic chemotaxis model with prevention of overcrowding. Adv. in Appl. Math. 26 (2001) 281-301
    • (2001) Adv. in Appl. Math. , vol.26 , pp. 281-301
    • Hillen, T.1    Painter, K.J.2
  • 17
    • 63049107118 scopus 로고    scopus 로고
    • A user's guide to PDE models for chemotaxis
    • Hillen T., and Painter K.J. A user's guide to PDE models for chemotaxis. J. Math. Biol. 58 (2009) 183-217
    • (2009) J. Math. Biol. , vol.58 , pp. 183-217
    • Hillen, T.1    Painter, K.J.2
  • 18
    • 0035646454 scopus 로고    scopus 로고
    • Blow-up in a chemotaxis model without symmetry assumptions
    • Horstmann D., and Wang G. Blow-up in a chemotaxis model without symmetry assumptions. European J. Appl. Math. 12 (2001) 159-177
    • (2001) European J. Appl. Math. , vol.12 , pp. 159-177
    • Horstmann, D.1    Wang, G.2
  • 19
    • 18144371222 scopus 로고    scopus 로고
    • Boundedness vs. blow-up in a chemotaxis system
    • Horstmann D., and Winkler M. Boundedness vs. blow-up in a chemotaxis system. J. Differential Equations 215 (2005) 52-107
    • (2005) J. Differential Equations , vol.215 , pp. 52-107
    • Horstmann, D.1    Winkler, M.2
  • 20
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • Jäger W., and Luckhaus S. On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc. 329 (1992) 819-824
    • (1992) Trans. Amer. Math. Soc. , vol.329 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 21
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • Keller E.F., and Segel L.A. Initiation of slime mold aggregation viewed as an 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
  • 22
    • 41449086239 scopus 로고    scopus 로고
    • On the global existence of solutions to an aggregation model
    • Kowalczyk R., and Szymańska Z. On the global existence of solutions to an aggregation model. J. Math. Anal. Appl. 343 (2008) 379-398
    • (2008) J. Math. Anal. Appl. , vol.343 , pp. 379-398
    • Kowalczyk, R.1    Szymańska, Z.2
  • 23
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • Lachowicz M. Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours. Math. Models Methods Appl. Sci. 15 (2005) 1667-1683
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1667-1683
    • Lachowicz, M.1
  • 24
    • 84873049159 scopus 로고    scopus 로고
    • Towards microscopic and nonlocal models of tumour invasion of tissue
    • Bellomo N., Chaplain M., and De Angelis E. (Eds), Birkhäuser, Boston
    • Lachowicz M. Towards microscopic and nonlocal models of tumour invasion of tissue. In: Bellomo N., Chaplain M., and De Angelis E. (Eds). Selected Topics in Cancer Modeling (2008), Birkhäuser, Boston 49-63
    • (2008) Selected Topics in Cancer Modeling , pp. 49-63
    • Lachowicz, M.1
  • 25
    • 0003223550 scopus 로고
    • Linear and Quasi-Linear Equations of Parabolic Type
    • Amer. Math. Soc., Providence, RI
    • Ladyzenskaja O.A., Solonnikov V.A., and Ural'ceva N.N. Linear and Quasi-Linear Equations of Parabolic Type. Amer. Math. Soc. Transl. vol. 23 (1968), Amer. Math. Soc., Providence, RI
    • (1968) Amer. Math. Soc. Transl. , vol.23
    • Ladyzenskaja, O.A.1    Solonnikov, V.A.2    Ural'ceva, N.N.3
  • 26
    • 71749113781 scopus 로고    scopus 로고
    • Global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology
    • Liţcanu G., and Morales-Rodrigo C. Global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology. Nonlinear Anal. 72 (2010) 77-98
    • (2010) Nonlinear Anal. , vol.72 , pp. 77-98
    • Liţcanu, G.1    Morales-Rodrigo, C.2
  • 29
    • 0010786688 scopus 로고    scopus 로고
    • Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
    • Nagai T. Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains. J. Inequal. Appl. 6 (2001) 37-55
    • (2001) J. Inequal. Appl. , vol.6 , pp. 37-55
    • Nagai, T.1
  • 30
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks
    • Othmer H.G., and Stevens A. Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks. SIAM J. Appl. Math. 57 (1997) 1044-1081
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 31
    • 0032767250 scopus 로고    scopus 로고
    • Extracellular matrix concentration exerts selection pressure on invasive cells
    • Perumpanani A.J., and Byrne H.M. Extracellular matrix concentration exerts selection pressure on invasive cells. Eur. J. Cancer 8 (1999) 1274-1280
    • (1999) Eur. J. Cancer , vol.8 , pp. 1274-1280
    • Perumpanani, A.J.1    Byrne, H.M.2
  • 33
    • 34547463400 scopus 로고    scopus 로고
    • Time global existence and asymptotic behavior of solutions to degenerate quasi-linear parabolic systems of chemotaxis
    • Sugiyama Y. Time global existence and asymptotic behavior of solutions to degenerate quasi-linear parabolic systems of chemotaxis. Differential Integral Equations 20 (2007) 133-180
    • (2007) Differential Integral Equations , vol.20 , pp. 133-180
    • Sugiyama, Y.1
  • 34
  • 35
    • 58349114231 scopus 로고    scopus 로고
    • Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue
    • Szymańska Z., Urbański J., and Marciniak-Czochra A. Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue. J. Math. Biol. 58 (2009) 819-844
    • (2009) J. Math. Biol. , vol.58 , pp. 819-844
    • Szymańska, Z.1    Urbański, J.2    Marciniak-Czochra, A.3
  • 36
    • 59349107182 scopus 로고    scopus 로고
    • Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source
    • Tao Y. Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source. J. Math. Anal. Appl. 354 (2009) 60-69
    • (2009) J. Math. Anal. Appl. , vol.354 , pp. 60-69
    • Tao, Y.1
  • 37
    • 77950873803 scopus 로고    scopus 로고
    • Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis
    • 10.1016/j.nonrwa.2009.05.005
    • Tao Y. Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis. Nonlinear Anal. Real World Appl. (2009) 10.1016/j.nonrwa.2009.05.005
    • (2009) Nonlinear Anal. Real World Appl.
    • Tao, Y.1
  • 38
    • 56349131380 scopus 로고    scopus 로고
    • Global solution for a chemotactic-haptotactic model of cancer invasion
    • Tao Y., and Wang M. Global solution for a chemotactic-haptotactic model of cancer invasion. Nonlinearity 21 (2008) 2221-2238
    • (2008) Nonlinearity , vol.21 , pp. 2221-2238
    • Tao, Y.1    Wang, M.2
  • 39
    • 73349141980 scopus 로고    scopus 로고
    • A combined chemotaxis-haptotaxis system: The role of logistic source
    • Tao Y., and Wang M. A combined chemotaxis-haptotaxis system: The role of logistic source. SIAM J. Math. Anal. 41 (2009) 1533-1558
    • (2009) SIAM J. Math. Anal. , vol.41 , pp. 1533-1558
    • Tao, Y.1    Wang, M.2
  • 40
    • 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
  • 42
    • 41149130747 scopus 로고    scopus 로고
    • Global existence for an age and spatially structured haptotaxis model with nonlinear age-boundary conditions
    • Walker C. Global existence for an age and spatially structured haptotaxis model with nonlinear age-boundary conditions. European J. Appl. Math. 19 (2008) 113-147
    • (2008) European J. Appl. Math. , vol.19 , pp. 113-147
    • Walker, C.1
  • 43
    • 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
  • 44
    • 51249105317 scopus 로고    scopus 로고
    • Chemotaxis with logistic source: Very weak global solutions and their boundedness properties
    • Winkler M. Chemotaxis with logistic source: Very weak global solutions and their boundedness properties. J. Math. Anal. Appl. 348 (2008) 708-729
    • (2008) J. Math. Anal. Appl. , vol.348 , pp. 708-729
    • Winkler, M.1
  • 45
    • 9244236567 scopus 로고    scopus 로고
    • Global attractor for a chemotaxis model with prevention of overcrowding
    • Wrzosek D. Global attractor for a chemotaxis model with prevention of overcrowding. Nonlinear Anal. 59 (2004) 1293-1310
    • (2004) Nonlinear Anal. , vol.59 , pp. 1293-1310
    • Wrzosek, D.1


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