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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) : 733744. doi: 10.3934/proc.2015.0733 
[2] 
Adam Sullivan, Folashade Agusto, Sharon Bewick, Chunlei Su, Suzanne Lenhart, Xiaopeng Zhao. A mathematical model for withinhost Toxoplasma gondii invasion dynamics. Mathematical Biosciences & Engineering, 2012, 9 (3) : 647662. doi: 10.3934/mbe.2012.9.647 
[3] 
Florian Rupp, Jürgen Scheurle. Analysis of a mathematical model for jellyfish blooms and the cambric fish invasion. Conference Publications, 2013, 2013 (special) : 663672. doi: 10.3934/proc.2013.2013.663 
[4] 
Kentarou Fujie. Global asymptotic stability in a chemotaxisgrowth model for tumor invasion. Discrete & Continuous Dynamical Systems  S, 2020, 13 (2) : 203209. doi: 10.3934/dcdss.2020011 
[5] 
Philip Gerlee, Alexander R. A. Anderson. Diffusionlimited tumour growth: Simulations and analysis. Mathematical Biosciences & Engineering, 2010, 7 (2) : 385400. doi: 10.3934/mbe.2010.7.385 
[6] 
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 
[7] 
Eduardo IbargüenMondragón, Lourdes Esteva, Edith Mariela BurbanoRosero. Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma. Mathematical Biosciences & Engineering, 2018, 15 (2) : 407428. doi: 10.3934/mbe.2018018 
[8] 
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 
[9] 
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020264 
[10] 
Herbert Koch. Partial differential equations with nonEuclidean geometries. Discrete & Continuous Dynamical Systems  S, 2008, 1 (3) : 481504. doi: 10.3934/dcdss.2008.1.481 
[11] 
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 
[12] 
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 
[13] 
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 
[14] 
Barbara AbrahamShrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 577582. doi: 10.3934/dcdss.2018032 
[15] 
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 
[16] 
Marek Bodnar, Monika Joanna Piotrowska, Urszula Foryś, Ewa Nizińska. Model of tumour angiogenesis  analysis of stability with respect to delays. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1935. doi: 10.3934/mbe.2013.10.19 
[17] 
John R. King, Judith PérezVelázquez, H.M. Byrne. Singular travelling waves in a model for tumour encapsulation. Discrete & Continuous Dynamical Systems  A, 2009, 25 (1) : 195230. doi: 10.3934/dcds.2009.25.195 
[18] 
Russell Betteridge, Markus R. Owen, H.M. Byrne, Tomás Alarcón, Philip K. Maini. The impact of cell crowding and active cell movement on vascular tumour growth. Networks & Heterogeneous Media, 2006, 1 (4) : 515535. doi: 10.3934/nhm.2006.1.515 
[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] 
M.A.J Chaplain, G. Lolas. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Networks & Heterogeneous Media, 2006, 1 (3) : 399439. doi: 10.3934/nhm.2006.1.399 
2018 Impact Factor: 1.313
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