Amann, H. (1995) Linear and Quasilinear Parabolic Problems, Vol. I, Birkhäuser, Basel.
Arendt, W. & Bu, S. (2004) Operator-valued Fourier multipliers on periodic Besov spaces and applications. Proc. Edinb. Math. Soc. 47, 15–33.
Bazaliy, B. & Friedman, A. (2003) Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: An application to a model of tumor growth. Indiana Univ. Math. J. 52, 1265–1304.
Borisovich, A. & Friedman, A. (2005) Symmetry-breaking bifurcations for free boundary problems. Indiana. Uni. Math. J. 54, 927–947.
Byrne, H. (1999) A weakly nonlinear analysis of a model of avascular solid tumour growth. J. Math. Biol. 39, 59–89.
Byrne, H. & Chaplain, M. (1996) Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Modelling 24, 1–17.
Byrne, H. & Chaplain, M. (1997) Free boundary value problems associated with the growth and development of multicellular spheroids. Eur. J. Appl. Math. 8, 639–658.
Chen, X., Cui, S. & Friedman, A. (2005) A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior. Trans. Amer. Math. Soc. 357, 4771–4804.
Crandall, M. & Rabinowitz, P. (1971) Bifurcation from simple eigenvalues. J. Funct. Anal. 8, 321–340.
Cui, S. & Escher, J. (2007) Bifurcation analysis of an elliptic free boundary problme modeling stationary growth of avascular tumors. SIAM J. Math. Anal. 39, 210–235.
Cui, S. & Escher, J. (2009) Well-posedness and stability of a multidimensional tumor growth model. Arch. Ration. Mech. Anal. 191, 173–193.
Cui, S. & Friedman, A. (2003) A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Trans. Amer. Math. Soc. 355, 3537–3590.
Escher, J. (2004) Classical solutions to a moving boundary problem for an elliptic-parabolic system. Interfaces Free Bound. 6, 175–193.
Escher, J. & Matioc, B. (2008) On periodic Stokesian Hele-Shaw flows with surface tension. Eur. J. Appl. Math. 19, 717–734.
Escher, J. & Matioc, B. (2009) Existence and stability results for periodic Stokesian Hele-Shaw flows. SIAM J. Math. Anal. 40, 1992–2006.
Escher, J. & Simonett, G. (1997) Classical solutions for Hele-Shaw models with surface tension. Adv. Differ. Equ. 2, 619–642.
Friedman, A. (2007) Mathematical analysis and challenges arising from models of tumor growth. Math. Models Methods Appl. Sci. 17, 1751–1772.
Friedman, A. & Hu, B. (2006) Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Arch. Ration. Mech. Anal. 180, 293–330.
Friedman, A. & Hu, B. (2007) Bifurcation for a free boundary problem modeling tumor growth by stokes equation. SIAM J. Math. Anal. 39, 174–194.
Friedman, A. & Reitich, F. (1999) Analysis of a mathematical model for the growth of tumors. J. Math. Biol. 38, 262–284.
Greenspan, H. (1975) On the growth and stability of cell cultures and solid tumors. J. Theor. Biol. 56, 229–242.
Kim, J., Stein, R. & O'haxe, M. (2004) Three-dimensional in vitro tissue culture models for breast cancer – a review. Breast Cancer Res. Treat. 149, 1–11.
Kyle, A., Chan, C. & Minchinton, A. (1999) Characterization of three-dimensional tissue cultures using electrical impedance spectroscopy. Biophysical J. 76, 2640–2648.
Lowengrub, J.et al. (2010) Nonlinear modeling of cancer: Bridging the gap between cells and tumours. Nonlinearity 23, R1–R91.
Lunardi, A. (1995) Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel.
Mueller-Klieser, W. (1997) Three dimensional cell cultures: From molecular mechanisms to clinical applications. Am. J. Cell Physiol. 273, 1109–1123.
Roose, T., Chapman, S. & Maini, P. (2007) Mathematical models of avascular tumor growth. SIAM Rev. 49, 179–208.
Schmeisser, H. & Triebel, H. (1987) Topics in Fourier Analysis and Function Spaces, John Wiley and Sons, New York.
Wu, J. & Cui, S. (2009) Asymptotic stability of stationary solutions of a free boundary problem modeling the growth of tumors with fluid tissues. SIAM J. Math. Anal. 41, 391–414.
Wu, J. & Zhou, F. (2012) Bifurcation analysis of a free boundary problem modelling tumour growth under the action of inhibitors. Nonlinearity 25, 2971–2991.
Wu, J. & Zhou, F. (2013) Asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors. Trans. Amer. Math. Soc. 365, 4181–4207.
Zhou, F., Escher, J. & Cui, S. (2008) Bifurcation for a free boundary problem with surface tension modeling the growth of multi-layer tumors. J. Math. Anal. Appl. 337, 443–457.
Zhou, F., Escher, J. & Cui, S. (2008) Well-posedness and stability of a free boundary problem modeling the growth of multi-layer tumors. J. Differ. Equ. 244, 2909–2933.