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Multiphase modeling and qualitative analysis of the growth of tumor cords
1.  Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy 
[1] 
Junde Wu, Shangbin Cui. Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth. Discrete & Continuous Dynamical Systems  A, 2010, 26 (2) : 737765. doi: 10.3934/dcds.2010.26.737 
[2] 
Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete & Continuous Dynamical Systems  B, 2011, 15 (1) : 293308. doi: 10.3934/dcdsb.2011.15.293 
[3] 
Shihe Xu, Yinhui Chen, Meng Bai. Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 9971008. doi: 10.3934/dcdsb.2016.21.997 
[4] 
Shihe Xu, Meng Bai, Fangwei Zhang. Analysis of a free boundary problem for tumor growth with GibbsThomson relation and time delays. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 117. doi: 10.3934/dcdsb.2017213 
[5] 
Fujun Zhou, Shangbin Cui. Wellposedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete & Continuous Dynamical Systems  A, 2008, 21 (3) : 929943. doi: 10.3934/dcds.2008.21.929 
[6] 
Yueping Dong, Rinko Miyazaki, Yasuhiro Takeuchi. Mathematical modeling on helper T cells in a tumor immune system. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 5572. doi: 10.3934/dcdsb.2014.19.55 
[7] 
T.L. Jackson. A mathematical model of prostate tumor growth and androgenindependent relapse. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 187201. doi: 10.3934/dcdsb.2004.4.187 
[8] 
J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263278. doi: 10.3934/mbe.2013.10.263 
[9] 
Hyun Geun Lee, Yangjin Kim, Junseok Kim. Mathematical model and its fast numerical method for the tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 11731187. doi: 10.3934/mbe.2015.12.1173 
[10] 
Avner Friedman. Free boundary problems arising in biology. Discrete & Continuous Dynamical Systems  B, 2018, 23 (1) : 193202. doi: 10.3934/dcdsb.2018013 
[11] 
Anatoli Babin, Alexander Figotin. Some mathematical problems in a neoclassical theory of electric charges. Discrete & Continuous Dynamical Systems  A, 2010, 27 (4) : 12831326. doi: 10.3934/dcds.2010.27.1283 
[12] 
Avner Friedman. Free boundary problems for systems of Stokes equations. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14551468. doi: 10.3934/dcdsb.2016006 
[13] 
Noriaki Yamazaki. Almost periodicity of solutions to free boundary problems. Conference Publications, 2001, 2001 (Special) : 386397. doi: 10.3934/proc.2001.2001.386 
[14] 
Serena Dipierro, Enrico Valdinoci. (Non)local and (non)linear free boundary problems. Discrete & Continuous Dynamical Systems  S, 2018, 11 (3) : 465476. doi: 10.3934/dcdss.2018025 
[15] 
Jinzhi Wang, Yuduo Zhang. Solving the seepage problems with free surface by mathematical programming method. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 351357. doi: 10.3934/naco.2015.5.351 
[16] 
Harald Garcke, Kei Fong Lam. Analysis of a CahnHilliard system with nonzero Dirichlet conditions modeling tumor growth with chemotaxis. Discrete & Continuous Dynamical Systems  A, 2017, 37 (8) : 42774308. doi: 10.3934/dcds.2017183 
[17] 
J. I. Díaz, J. F. Padial. On a freeboundary problem modeling the action of a limiter on a plasma. Conference Publications, 2007, 2007 (Special) : 313322. doi: 10.3934/proc.2007.2007.313 
[18] 
Weiqing Xie. A free boundary problem arising from the process of Czochralski crystal growth. Conference Publications, 2001, 2001 (Special) : 380385. doi: 10.3934/proc.2001.2001.380 
[19] 
Elena IzquierdoKulich, José Manuel NietoVillar. Mesoscopic model for tumor growth. Mathematical Biosciences & Engineering, 2007, 4 (4) : 687698. doi: 10.3934/mbe.2007.4.687 
[20] 
Svetlana BunimovichMendrazitsky, Yakov Goltser. Use of quasinormal form to examine stability of tumorfree equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529547. doi: 10.3934/mbe.2011.8.529 
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