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Modelling cell populations with spatial structure: Steady state and treatmentinduced evolution
A mathematical model of prostate tumor growth and androgenindependent relapse
1.  Department of Mathematics, University of Michigan, Ann Arbor, Michigan 
[1] 
Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591608. doi: 10.3934/mbe.2013.10.591 
[2] 
Alacia M. Voth, John G. Alford, Edward W. Swim. Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer. Mathematical Biosciences & Engineering, 2017, 14 (3) : 777804. doi: 10.3934/mbe.2017043 
[3] 
Erica M. Rutter, Yang Kuang. Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 10011021. doi: 10.3934/dcdsb.2017050 
[4] 
HsiuChuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems  B, 2016, 21 (4) : 12791295. doi: 10.3934/dcdsb.2016.21.1279 
[5] 
Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete & Continuous Dynamical Systems  B, 2013, 18 (4) : 945967. doi: 10.3934/dcdsb.2013.18.945 
[6] 
Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020426 
[7] 
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 
[8] 
Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems  B, 2013, 18 (4) : 891914. doi: 10.3934/dcdsb.2013.18.891 
[9] 
Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 12231240. doi: 10.3934/mbe.2016040 
[10] 
Frederic Abergel, Remi Tachet. A nonlinear partial integrodifferential equation from mathematical finance. Discrete & Continuous Dynamical Systems  A, 2010, 27 (3) : 907917. doi: 10.3934/dcds.2010.27.907 
[11] 
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020264 
[12] 
Herbert Koch. Partial differential equations with nonEuclidean geometries. Discrete & Continuous Dynamical Systems  S, 2008, 1 (3) : 481504. doi: 10.3934/dcdss.2008.1.481 
[13] 
Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete & Continuous Dynamical Systems  A, 2006, 15 (3) : 703723. doi: 10.3934/dcds.2006.15.703 
[14] 
Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 10531065. doi: 10.3934/cpaa.2009.8.1053 
[15] 
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 515557. doi: 10.3934/dcdsb.2010.14.515 
[16] 
Barbara AbrahamShrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 577582. doi: 10.3934/dcdss.2018032 
[17] 
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31273144. doi: 10.3934/dcdsb.2017167 
[18] 
Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 147159. doi: 10.3934/dcdsb.2004.4.147 
[19] 
Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure & Applied Analysis, 2011, 10 (5) : 13451360. doi: 10.3934/cpaa.2011.10.1345 
[20] 
Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel. On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells. Mathematical Biosciences & Engineering, 2015, 12 (1) : 163183. doi: 10.3934/mbe.2015.12.163 
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