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DOI:

https://doi.org/10.12775/TMNA.2021.064

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Bibliografia

H.M. Byrne and M.A. Chaplain, Growth of nonnecrotic tumors in the presence and absence of inhibitors, Math. Biosci. 130 (1995), 151–181.

P. Chossat and R. Lauterbach, Methods in Equivariant Bifurcations and Dynamical Systems, World Scientific Publishing Co., Inc., River Edge, NJ, 2000.

P. Chossat, R. Lauterbach and I. Melbourne, Steady-state bifurcation with O(3)symmetry, Arch. Rational Mech. Anal. 113 (1990), 313–376.

G. Cicogna, Symmetry breakdown from bifurcation, Lett. Nuovo Cimento 31 (1981), no. 2, 600–602.

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Anal., 8 (1971), 321–340.

S. Cui and J. Escher, Bifurcation analysis of an elliptic free boundary problem modelling the growth of avascular tumors, SIAM J. Math. Anal. 39 (2007), 210–235.

J. Escher and A.-V. Matioc, Bifurcation analysis for a free boundary problem modeling tumor growth, Arch. Math. (Basel) 97 (2011), 79–90.

B. Fiedler, J. Hell and B. Smith, Anisotropic Einstein data with isotropic non negative prescribed scalar curvature, Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), 401–428.

M.A. Fontelos and A. Friedman, Symmetry-breaking bifurcations of free boundary problems in three dimensions, Asymptot. Anal. 35 (2003), 187–206.

S.J. Franks, H.M. Byrne, J.R. King, J.C.E. Underwood and C.E. Lewis, Modelling the early growth of ductal carcinoma in situ of the breast, J. Math. Biol. 47 (2003), 424–452.

S.J. Franks, H.M. Byrne, H.S. Mudhar, J.C. Underwood and C.E. Lewis, Mathematical modelling of comedo ductal carcinoma in situ of the breast, Math. Med. Biol. 20 (2003), p. 277.

S.J. Franks, H.M. Byrne, J.C.E. Underwood and C.E. Lewis, Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast, J. Theoret. Biol. 232 (2005), 523–543.

A. Friedman, A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth, Interfaces Free Bound. 8 (2006), 247–261.

A. Friedman, Free boundary problems associated with multiscale tumor models, Math. Model. Nat. Phenom. 4 (2009), 134–155.

A. Friedman and B. Hu, Bifurcation from stability to instability for a free boundary problem arising in a tumor model, Arch. Ration. Mech. Anal. 180 (2006), 293–330.

A. Friedman and B. Hu, Bifurcation for a free boundary problem modeling tumor growth by Stokes equation, SIAM J. Math. Anal. 39 (2007), 174–194.

A. Friedman and B. Hu, Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation, J. Math. Anal. Appl. 327 (2007), 643–664.

A. Friedman and B. Hu, Stability and instability of Liapunov–Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model, Trans. Amer. Math. Soc. 360 (2008), 5291–5342.

A. Friedman and F. Reitich, Analysis of a mathematical model for the growth of tumors, J. Math. Biol. 38 (1999), 262–284.

A. Friedman and F. Reitich, Symmetry-breaking bifurcation of analytic solutions to free boundary problems: an application to a model of tumor growth, Trans. Amer. Math. Soc. 353 (2001), 1587–1634.

M. Golubitsky, I. Stewart and D. Schaeffer, Singularities and Groups in Bifurcation Theory, vol. II, Springer–Verlag, New York, 1988.

W. Hao, J.D. Hauenstein, B. Hu, Y. Liu, A.J. Sommese and Y.-T. Zhang, Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core, Nonlinear Anal. Real World Appl. 13 (2012), 694–709.

T.J. Healey and S. Dharmavaram, Symmetry-breaking global bifurcation in a surface continuum phase-field model for lipid bilayer vesicles, SIAM J. Math. Anal. 49 (2017), 1027–1059.

Y. Huang, Z. Zhang and B. Hu, Bifurcation for a free-boundary tumor model with angiogenesis, Nonlinear Anal. Real World Appl. 35 (2017), 483–502.

E. Ihrig and M. Golubitsky, Pattern selection with O(3) symmetry, Phys. D, 13 (1984), 1–33.

H. Kielhöfer, Bifurcation Theory. An Introduction with Applications to Partial Differential Equations, Springer, New York, second edition, 2012.

F. Li and B. Liu, Bifurcation for a free boundary problem modeling the growth of tumors with a drug induced nonlinear proliferation rate, J. Differential Equations 263 (2017), 7627–7646.

J.S. Lowengrub, H.B. Frieboes, F. Jin, Y.-L. Chuang, X. Li, P. Macklin, S.M. Wise and V. Cristini, Nonlinear modelling of cancer: bridging the gap between cells and tumours, Nonlinearity 23 (2010), R1–R91.

H. Pan and R. Xing, Bifurcation for a free boundary problem modeling tumor growth with ECM and MDE interactions, Nonlinear Anal. Real World Appl. 43 (2018), 362–377.

D.H. Sattinger, Bifurcation from rotationally invariant states, J. Math. Phys. 19 (1978), 1720–1732.

D.H. Sattinger, Group-Theoretic Methods in Bifurcation Theory, Lect. Notes Math., vol. 762, Springer, Berlin, 1979.

R.M. Sutherland, Cell and environment interactions in tumor microregions: the multicell spheroid model, Science 240 (1988), 177–184.

J.E. Tanner, A. Forté and C. Panchal, Nucleosomes bind fibroblast growth factor-2 for increased angiogenesis in vitro and in vivo, Molecular Cancer Research 2 (2004), 281–288.

A. Vanderbauwhede, Local Bifurcation and Symmetry, Pitman, Boston, MA, 1982.

Z. Wang, Bifurcation for a free boundary problem modeling tumor growth with inhibitors, Nonlinear Anal. Real World Appl. 19 (2014), 45–53.

Z. Wang, J. Xu and J. Li, Bifurcation analysis for a free boundary problem modeling growth of solid tumor with inhibitors, Commun. Math. Res. 33 (2017), 85–96.

Z. Wang, S. Xu and H. Song, Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor, Discrete Contin. Dyn. Syst. Ser. B 23 (2018), 2593–2605.

D. Westreich, Bifurcation at eigenvalues of odd multiplicity, Proc. Amer. Math. Soc. 41 (1973), 609–614.

J. Wu, Stationary solutions of a free boundary problem modeling the growth of tumors with Gibbs–Thomson relation, J. Differential Equations 260 (2016), 5875–5893.

J. Wu, Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors, Discrete Contin. Dyn. Syst. 39 (2019), 3399–3411.

J. Wu and S. Cui, Bifurcation analysis of a mathematical model for the growth of solid tumors in the presence of external inhibitors, Math. Methods Appl. Sci. 38 (2015), 1813–1823.

J. Wu and F. Zhou, Bifurcation analysis of a free boundary problem modelling tumour growth under the action of inhibitors, Nonlinearity 25 (2012), 2971–2991.

H. Zhang, C. Qu, and B. Hu, Bifurcation for a free boundary problem modeling a protocell, Nonlinear Anal., 70 (2009), 2779–2795.

J. Zheng and R. Xing, Bifurcation for a free-boundary tumor model with extracellular matrix and matrix degrading enzymes, J. Differential Equations 268 (2020), 3152–3170.

F. Zhou and S. Cui, Bifurcation for a free boundary problem modeling the growth of multi-layer tumors, Nonlinear Anal. 68 (2008), 2128–2145.

F. Zhou, J. Escher and S. Cui, Bifurcation for a free boundary problem with surface tension modeling the growth of multi-layer tumors, J. Math. Anal. Appl. 337 (2008), 443–457.

Opublikowane

2022-08-31

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& . Topological Methods in Nonlinear Analysis [online]. 31 sierpień 2022, T. 60, nr 1, s. 387–412. [udostępniono 21.11.2024]. DOI 10.12775/TMNA.2021.064.

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