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Volumn 12, Issue 4, 2009, Pages 731-767

A model describing the growth and the size distribution of multiple metastatic tumors

Author keywords

Asymptotic behavior; McKendrick Von Foerster equation; Metastatic tumors; Relative entropy; WENO scheme

Indexed keywords


EID: 73649086252     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.12.731     Document Type: Article
Times cited : (19)

References (15)
  • 2
    • 60349096256 scopus 로고    scopus 로고
    • Mathematical and numerical analysis for a model of growing metastatic tumors
    • Dominique Barbolosi, Assia Benabdallah, Florence Hubert and Federico Verga, Mathematical and numerical analysis for a model of growing metastatic tumors, Math. Biosci., 218 (2009), 1-14.
    • (2009) Math. Biosci , vol.218 , pp. 1-14
    • Barbolosi, D.1    Benabdallah, A.2    Hubert, F.3    Verga, F.4
  • 3
    • 0034254401 scopus 로고    scopus 로고
    • Modelling and mathematical problems related to tumor evolution and its interaction with the immune system
    • Nicola Bellomo and Luidgi Preziosi, Modelling and mathematical problems related to tumor evolution and its interaction with the immune system, Math. Comput. Modelling, 32 (2000), 413-452.
    • (2000) Math. Comput. Modelling , vol.32 , pp. 413-452
    • Bellomo, N.1    Preziosi, L.2
  • 4
    • 0036588843 scopus 로고    scopus 로고
    • The Beker-Döring system and its Lifshitz-Slyozov limit
    • electronic
    • Jean-Francois Collet, Thierry Goudon, Frédéric Poupaud and Alexis Vasseur, The Beker-Döring system and its Lifshitz-Slyozov limit, SIAM J. Appl. Math., 62 (2002), 1488-1500 (electronic).
    • (2002) SIAM J. Appl. Math , vol.62 , pp. 1488-1500
    • Collet, J.-F.1    Goudon, T.2    Poupaud, F.3    Vasseur, A.4
  • 5
    • 0022768062 scopus 로고
    • A cell kinetics justification for Gompertz' equation
    • C. L. Frenzen and J. D. Murray, A cell kinetics justification for Gompertz' equation, SIAM J. Appl. Math., 46 (1986), 614-629.
    • (1986) SIAM J. Appl. Math , vol.46 , pp. 614-629
    • Frenzen, C.L.1    Murray, J.D.2
  • 6
    • 33845633449 scopus 로고    scopus 로고
    • Invariants and exponential rate of convergence to steady state in the renewal equation
    • and BenoîtPerthame
    • Piotr Gwiazda and BenoîtPerthame, Invariants and exponential rate of convergence to steady state in the renewal equation, Markov Process. Related Fields, 12 (2006), 413-424.
    • (2006) Markov Process. Related Fields , vol.12 , pp. 413-424
    • Gwiazda, P.1
  • 7
    • 0025687227 scopus 로고
    • A nonlinear structured population model of tumor growth with quiescence
    • Mats Gyllenberg and Glenn F. Webb, A nonlinear structured population model of tumor growth with quiescence, J. Math. Biol., 28 (1990), 671-694.
    • (1990) J. Math. Biol , vol.28 , pp. 671-694
    • Gyllenberg, M.1    Webb, G.F.2
  • 8
    • 0024435736 scopus 로고
    • Quiescence as an explanation of gompertzian tumor growth
    • Mats Gyllenberg and Glenn F. Webb, Quiescence as an explanation of gompertzian tumor growth, Growth Development & Aging, 53 (1989), 25-33.
    • (1989) Growth Development & Aging , vol.53 , pp. 25-33
    • Gyllenberg, M.1    Webb, G.F.2
  • 9
    • 0034696450 scopus 로고    scopus 로고
    • A dynamical model for the growth and size distribution of multiple metastatic tumors
    • K. Iwata, K. Kawasaki and N. Shigesada, A dynamical model for the growth and size distribution of multiple metastatic tumors, Journal of Theoretical Biology, 203 (2000), 177-186.
    • (2000) Journal of Theoretical Biology , vol.203 , pp. 177-186
    • Iwata, K.1    Kawasaki, K.2    Shigesada, N.3
  • 10
    • 0041736643 scopus 로고    scopus 로고
    • Combining Gompertzian growth and cell population dynamics
    • Frank Kozusko and Željko Bajzer, Combining Gompertzian growth and cell population dynamics, Math. Biosci., 185 (2003), 153-167.
    • (2003) Math. Biosci , vol.185 , pp. 153-167
    • Kozusko, F.1    Bajzer, Z.2
  • 11
    • 73649121527 scopus 로고    scopus 로고
    • Principe D'entropie Géné ralisée et Dynamique de Populations Structurées
    • Thèse de doctorat, Université Paris IX-Dauphine, November
    • Philippe Michel, "Principe D'entropie Géné ralisée et Dynamique de Populations Structurées", Thèse de doctorat, Université Paris IX-Dauphine, November 2005.
    • (2005)
    • Michel, P.1
  • 12
    • 1842843699 scopus 로고    scopus 로고
    • General entropy equations for structured population models and scattering
    • Philippe Michel, Stéphane Mischler and Benoît Perthame, General entropy equations for structured population models and scattering, C. R. Math. Acad. Sci. Paris, 338 (2004), 697-702.
    • (2004) C. R. Math. Acad. Sci. Paris , vol.338 , pp. 697-702
    • Michel, P.1    Mischler, S.2    Perthame, B.3
  • 13
    • 36249025671 scopus 로고    scopus 로고
    • Transport Equations in Biology
    • Birkhäuser Verlag, Basel
    • Benoît Perthame, "Transport Equations in Biology", Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2007.
    • (2007) Frontiers in Mathematics
    • Perthame, B.1
  • 14
    • 73649141211 scopus 로고    scopus 로고
    • Giovanni Russo, High Order Shock Capturing Schemes for Balance Laws, In Numerical Solutions of Partial Differential Equations, pages 160-251, Advanced Courses in Mathematics - CRM Barcelona. Basel: Birkhäuser., 2009.
    • Giovanni Russo, "High Order Shock Capturing Schemes for Balance Laws", In "Numerical Solutions of Partial Differential Equations", pages 160-251, Advanced Courses in Mathematics - CRM Barcelona. Basel: Birkhäuser., 2009.
  • 15
    • 0000034725 scopus 로고    scopus 로고
    • Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws
    • Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Cetraro, of, Springer, Berlin
    • Chi-Wang Shu, "Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws", In "Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" (Cetraro, 1997), volume 1697 of Lecture Notes in Math., 325-432, Springer, Berlin, 1998.
    • (1997) Lecture Notes in Math , vol.1697 , pp. 325-432
    • Shu, C.-W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.