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Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology
1. | Division of Mathematics, University of Dundee, 23 Perth Road, Dundee, DD1 4HN, United Kingdom, United Kingdom, United Kingdom |
2. | Applied Computing, University of Dundee, Dundee, DD1 4HN, United Kingdom |
[1] |
Akisato Kubo, Hiroki Hoshino, Katsutaka Kimura. Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to a tumour invasion model. Conference Publications, 2015, 2015 (special) : 733-744. doi: 10.3934/proc.2015.0733 |
[2] |
Adam Sullivan, Folashade Agusto, Sharon Bewick, Chunlei Su, Suzanne Lenhart, Xiaopeng Zhao. A mathematical model for within-host Toxoplasma gondii invasion dynamics. Mathematical Biosciences & Engineering, 2012, 9 (3) : 647-662. doi: 10.3934/mbe.2012.9.647 |
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Florian Rupp, Jürgen Scheurle. Analysis of a mathematical model for jellyfish blooms and the cambric fish invasion. Conference Publications, 2013, 2013 (special) : 663-672. doi: 10.3934/proc.2013.2013.663 |
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Kentarou Fujie. Global asymptotic stability in a chemotaxis-growth model for tumor invasion. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 203-209. doi: 10.3934/dcdss.2020011 |
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Andrea Signori. Penalisation of long treatment time and optimal control of a tumour growth model of Cahn–Hilliard type with singular potential. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2519-2542. doi: 10.3934/dcds.2020373 |
[6] |
Philip Gerlee, Alexander R. A. Anderson. Diffusion-limited tumour growth: Simulations and analysis. Mathematical Biosciences & Engineering, 2010, 7 (2) : 385-400. doi: 10.3934/mbe.2010.7.385 |
[7] |
Matthias Ebenbeck, Harald Garcke, Robert Nürnberg. Cahn–Hilliard–Brinkman systems for tumour growth. Discrete and Continuous Dynamical Systems - S, 2021, 14 (11) : 3989-4033. doi: 10.3934/dcdss.2021034 |
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Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907 |
[9] |
Eduardo Ibargüen-Mondragón, Lourdes Esteva, Edith Mariela Burbano-Rosero. Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma. Mathematical Biosciences & Engineering, 2018, 15 (2) : 407-428. doi: 10.3934/mbe.2018018 |
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Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591-608. doi: 10.3934/mbe.2013.10.591 |
[11] |
Herbert Koch. Partial differential equations with non-Euclidean geometries. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : 481-504. doi: 10.3934/dcdss.2008.1.481 |
[12] |
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264 |
[13] |
Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703 |
[14] |
Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure and Applied Analysis, 2009, 8 (3) : 1053-1065. doi: 10.3934/cpaa.2009.8.1053 |
[15] |
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515 |
[16] |
Barbara Abraham-Shrauner. Exact solutions of nonlinear partial differential equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 577-582. doi: 10.3934/dcdss.2018032 |
[17] |
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167 |
[18] |
Runzhang Xu. Preface: Special issue on advances in partial differential equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : i-i. doi: 10.3934/dcdss.2021137 |
[19] |
Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1345-1360. doi: 10.3934/cpaa.2011.10.1345 |
[20] |
John R. King, Judith Pérez-Velázquez, H.M. Byrne. Singular travelling waves in a model for tumour encapsulation. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 195-230. doi: 10.3934/dcds.2009.25.195 |
2018 Impact Factor: 1.313
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