References
- Colli P, Gilardi G, Rocca E, et al. Vanishing viscosities and error estimate for a Cahn–Hilliard type phase field system related to tumor growth. Nonlinear Anal Real World Appl. 2015;26:93–108.
- Colli P, Gilardi G, Rocca E, et al. Asymptotic analyses and error estimates for a Cahn–Hilliard type phase field system modelling tumor growth. Discrete Contin Dyn Syst. 2017;10(1):37–54.
- Garcke H, Lam KF, Rocca E. Optimal control of treatment time in a diffuse interface model of tumor growth. Appl Math Optim. 2018;78:495–544.
- Elliott CM, Stuart AM. Viscous Cahn-Hilliard equation. II. Analysis. J Differ Equ. 1996;128:387–414.
- Byrne H. Modelling solid tumour growth using the theory of mixtures. Math Med Biol. 2003;20(4):341–366.
- Bassea B, Baguley BC, Marshall ES, et al. Modelling cell population growth with applications to cancer therapy in human tumour cell lines. Prog Biophys Mol Biol. 2004;85(2–3):353–368.
- Gatenby RA. Application of competition theory to tumour growth: implications for tumour biology and treatment. Eur J Cancer. 1996;32A(4):722–726.
- Bukhgeim AL, Klibanov MV. Uniqueness in the large class of multidimensional inverse problems. Soviet Math Dokl. 1981;24:244–247.
- Beilina L, Klibanov MV. Approximate global convergence and adaptivity for coefficient inverse problems. Springer: New York; 2012.
- Benabdallah A, Cristofol M, Gaitan P, et al. Inverse problem for a parabolic system with two components by measurements of one component. Appl Anal. 2009;88(5):683–709.
- Cristofol M, Gaitan P, Ramoul H. Inverse problems for a 2×2 reaction-diffusion system using a Carleman estimate with one observation. Inverse Problems. 2006;22(5):1561–1573.
- Imanuvilov OYu. Controllability of parabolic equations. Sb Math. 1995;186(6):109–132.
- Imanuvilov OYu, Yamamoto M. Lipschitz stability in inverse problems by Carleman estimates. Inverse Problems. 1998;14(5):1229–1245.
- Klibanov MV. Inverse problems in the ‘large’ and Carleman bounds. Differ Equ. 1984;20(6):755–760.
- Klibanov MV. Inverse problems and Carleman estimates. Inverse Problems. 1992;8(4):575–596.
- Klibanov MV. Carleman estimates and inverse problems in the last two decades. In: Colton D, Engl HW, Louis AK, McLaughlin JR, Rundell W, editors. Surveys on solution methods for inverse problems. Vienna: Springer; 2000. p. 119–146.
- Klibanov MV. Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. J Inverse Ill-Posed Probl. 2013;21(4):477–560.
- Klibanov MV, Timonov A. Carleman estimates for coefficient inverse problems and numerical applications. Utrecht: VSP; 2004.
- Baranibalan N, Sakthivel K, Balachandran K, et al. Inverse problems for the phase field system with one observation. Appl Anal. 2009;88(4):529–545.
- Baranibalan N, Sakthivel K, Balachandran K, et al. Reconstruction of two time independent coefficients in an inverse problem for a phase field system. Nonlinear Anal. 2010;72(6):2841–2851.
- Ainseba B, Bendahmane M, He M. Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology. NETW HETEROG MEDIA. 2015;10(2):369–385.
- Bellassoued M, Moufid C, Yamamoto M. A Carleman estimate for the linear magnetoelastic waves system and an inverse source problem in a bounded conductive medium. Appl Anal. 2019. doi:https://doi.org/10.1080/00036811.2019.1566530.
- Yamamoto M. Carleman estimates for parabolic equations and applications. Inverse Problems. 2009;25(12):123013 (75pp).
- Hasanov A. Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: weak solution approach. J Math Anal Appl. 2007;330(2):766–779.
- Sakthivel K, Gnanavel S, Hasanov A, et al. Identification of an unknown coefficient in KdV equation from final time measurement. J Inverse Ill-Posed Probl. 2016;24(4):469–487.
- Sakthivel K, Hasanov A. An inverse problem for the KdV equation with Neumann boundary measured data. J Inverse Ill-Posed Probl. 2017;26(1):133–151.
- Tikhonov A, Arsenin V. Solutions of ill-posed problems. Beijing: Geology Press; 1979.
- Lessoued J, Mahjoub M, Zemzemi N. Stability results for the parameter identification inverse problem in cardiac electrophysiology. Inverse Problems. 2016;32(11):115002 (28pp).
- Roubicek T. Nonlinear partial differential equations with applications. Berlin: Birkhäuser Verlag; 2005.
- Simon J. Compact sets in the space Lp(0,T;B). Ann Mat Pura Appl. 1986;146(1):65–96.
- Renardy M, Rogers B. An introduction to partial differential equations. New York: Springer-Verlag Inc; 2004. (Texts in applied mathematics).