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Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning
A reaction-diffusion system modeling the spread of resistance to an antimalarial drug
1. | Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex, France |
2. | Laboratoire de Paludologie, Institut de Recherche pour le Développement, B.P. 1386, Dakar, Senegal |
[1] |
Sebastian Aniţa, Vincenzo Capasso. Stabilization of a reaction-diffusion system modelling malaria transmission. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1673-1684. doi: 10.3934/dcdsb.2012.17.1673 |
[2] |
Manjun Ma, Xiao-Qiang Zhao. Monostable waves and spreading speed for a reaction-diffusion model with seasonal succession. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 591-606. doi: 10.3934/dcdsb.2016.21.591 |
[3] |
Juliette Bouhours, Grégroie Nadin. A variational approach to reaction-diffusion equations with forced speed in dimension 1. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 1843-1872. doi: 10.3934/dcds.2015.35.1843 |
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Matthieu Alfaro, Thomas Giletti. Varying the direction of propagation in reaction-diffusion equations in periodic media. Networks and Heterogeneous Media, 2016, 11 (3) : 369-393. doi: 10.3934/nhm.2016001 |
[5] |
Luisa Malaguti, Cristina Marcelli, Serena Matucci. Continuous dependence in front propagation of convective reaction-diffusion equations. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1083-1098. doi: 10.3934/cpaa.2010.9.1083 |
[6] |
Henri Berestycki, Luca Rossi. Reaction-diffusion equations for population dynamics with forced speed I - The case of the whole space. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 41-67. doi: 10.3934/dcds.2008.21.41 |
[7] |
Zhenguo Bai, Tingting Zhao. Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4063-4085. doi: 10.3934/dcdsb.2018126 |
[8] |
Henri Berestycki, Luca Rossi. Reaction-diffusion equations for population dynamics with forced speed II - cylindrical-type domains. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 19-61. doi: 10.3934/dcds.2009.25.19 |
[9] |
Yong Jung Kim, Wei-Ming Ni, Masaharu Taniguchi. Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3707-3718. doi: 10.3934/dcds.2013.33.3707 |
[10] |
C.B. Muratov. A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 867-892. doi: 10.3934/dcdsb.2004.4.867 |
[11] |
Ning Wang, Zhi-Cheng Wang. Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 1599-1646. doi: 10.3934/dcds.2021166 |
[12] |
Shangbing Ai, Wenzhang Huang, Zhi-An Wang. Reaction, diffusion and chemotaxis in wave propagation. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 1-21. doi: 10.3934/dcdsb.2015.20.1 |
[13] |
Elena Trofimchuk, Manuel Pinto, Sergei Trofimchuk. On the minimal speed of front propagation in a model of the Belousov-Zhabotinsky reaction. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1769-1781. doi: 10.3934/dcdsb.2014.19.1769 |
[14] |
M. Grasselli, V. Pata. A reaction-diffusion equation with memory. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1079-1088. doi: 10.3934/dcds.2006.15.1079 |
[15] |
Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405 |
[16] |
Keng Deng. On a nonlocal reaction-diffusion population model. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 65-73. doi: 10.3934/dcdsb.2008.9.65 |
[17] |
Piermarco Cannarsa, Giuseppe Da Prato. Invariance for stochastic reaction-diffusion equations. Evolution Equations and Control Theory, 2012, 1 (1) : 43-56. doi: 10.3934/eect.2012.1.43 |
[18] |
Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515 |
[19] |
Zhiting Xu, Yingying Zhao. A reaction-diffusion model of dengue transmission. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2993-3018. doi: 10.3934/dcdsb.2014.19.2993 |
[20] |
Martino Prizzi. A remark on reaction-diffusion equations in unbounded domains. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 281-286. doi: 10.3934/dcds.2003.9.281 |
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