Edit Profile (opens in new tab) Hillen, Thomas Co-Author Distance Author ID: hillen.thomas Published as: Hillen, Thomas; Hillen, T. Documents Indexed: 84 Publications since 1993, including 4 Books 2 Contributions as Editor · 1 Further Contribution Co-Authors: 77 Co-Authors with 74 Joint Publications 1,878 Co-Co-Authors all top 5 Co-Authors 12 single-authored 16 Painter, Kevin J. 9 Lewis, Mark Alun 5 de Vries, Gerda 5 Hadeler, Karl-Peter 4 Lutscher, Frithjof 4 Rhodes, Adam 4 Wang, Zhian 4 Winkler, Michael 3 Buttenschön, Andreas 3 Othmer, Hans G. 3 Preziosi, Luigi 3 Swan, Amanda C. 2 Bourlioux, Anne 2 Chauvière, Arnaud 2 Dolak, Yasmin 2 Enderling, Heiko 2 Giunta, Valeria 2 Gong, Jiafen 2 Müller, Johannes 2 Murtha, Albert D. 2 Olobatuyi, Oluwole 2 Potts, Jonathan R. 2 Surulescu, Christina 1 Baabdulla, Arwa Abdulla 1 Babak, Petro Panasovych 1 Bianchi, Arianna 1 Bica, Ion 1 Borsi, Iacopo 1 Bose, Christopher J. 1 Bowman, John C. 1 Burger, Martin 1 Chaplain, Mark A. J. 1 Ciarletta, Pasquale 1 Dawes, Adriana T. 1 Dawson, Anthony 1 Deutsch, Andreas 1 Diekmann, Odo 1 Dietz, Klaus 1 Dos Santos, Mairon M. 1 Engwer, Christian 1 Fasano, Antonio 1 Finlay, Chris 1 Freedman, Herbert Irving 1 Frei, Christoph 1 Gerisch, Alf 1 Greese, B. 1 Hahnfeldt, Philip J. 1 Hinow, Peter 1 Jung, Sungjune 1 Kim, Woo-Jong 1 Knappitsch, Markus 1 Konstorum, Anna 1 Leonard, I. Edward 1 Levine, Howard Allen 1 Liu, Wenxiang 1 Lowengrub, John Samuel 1 Loy, Nadia 1 McAneney, H. 1 Now, Hesung 1 O’Rourke, S. F. C. 1 Park, Ju An 1 Patel, Ashna 1 Potapov, Alex 1 Potapov, Alexei B. 1 Primicerio, Mario 1 Pugliese, Andrea 1 Rhodes, Meghan 1 Rohde, Christian 1 Schmeiser, Christian 1 Schönfisch, Birgitt H. 1 Shyntar, Alexandra 1 Stocks, Theresa 1 Stolarska, Magdalena A. 1 Thieme, Horst R. 1 Trucu, Dumitru 1 van Roessel, Henry J. 1 White, Diana 1 Xue, Chuan 1 Yi, Yingfei 1 Yoo, Joo-Yeon 1 Zielinski, Jeffery all top 5 Serials 14 Journal of Mathematical Biology 6 Bulletin of Mathematical Biology 5 SIAM Journal on Applied Mathematics 5 Discrete and Continuous Dynamical Systems. Series B 4 European Journal of Applied Mathematics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Mathematical Medicine and Biology 4 Journal of Theoretical Biology 3 Mathematical Methods in the Applied Sciences 3 The Canadian Applied Mathematics Quarterly 3 Journal of Biological Dynamics 2 Journal of Mathematical Analysis and Applications 2 SIAM Review 2 Mathematical Biosciences and Engineering 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Advances in Applied Mathematics 1 Physica D 1 Journal of Dynamics and Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Chaos 1 Nonlinear Analysis. Real World Applications 1 SIAM Journal on Applied Dynamical Systems 1 Oberwolfach Reports 1 Lecture Notes in Mathematics 1 Mathematical Modeling and Computation 1 Computational & Mathematical Methods in Medicine 1 Networks and Heterogeneous Media 1 AIMS Mathematics 1 Mathematics of Planet Earth 1 CMS/CAIMS Books in Mathematics all top 5 Fields 78 Biology and other natural sciences (92-XX) 59 Partial differential equations (35-XX) 13 Probability theory and stochastic processes (60-XX) 10 Dynamical systems and ergodic theory (37-XX) 7 Ordinary differential equations (34-XX) 5 Integral equations (45-XX) 5 Numerical analysis (65-XX) 4 General and overarching topics; collections (00-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 75 Publications have been cited 3,040 times in 1,802 Documents Cited by ▼ Year ▼ A user’s guide to PDE models for chemotaxis. Zbl 1161.92003Hillen, T.; Painter, K. J. 844 2009 Volume-filling and quorum-sensing in models for chemosensitive movement. Zbl 1057.92013Painter, Kevin J.; Hillen, Thomas 330 2002 The diffusion limit of transport equations. II: Chemotaxis equations. Zbl 1103.35098Othmer, Hans G.; Hillen, Thomas 169 2002 Global existence for a parabolic chemotaxis model with prevention of overcrowding. Zbl 0998.92006Hillen, T.; Painter, K. 160 2001 The diffusion limit of transport equations derived from velocity-jump processes. Zbl 1002.35120Hillen, Thomas; Othmer, Hans G. 155 2000 Spatio-temporal chaos in a chemotaxis model. Zbl 1255.37026Painter, Kevin J.; Hillen, Thomas 114 2011 Pattern formation in prey-taxis systems. Zbl 1315.92064Lee, J. M.; Hillen, T.; Lewis, M. A. 90 2009 Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204Hillen, Thomas; Painter, Kevin J.; Winkler, Michael 83 2013 Classical solutions and pattern formation for a volume filling chemotaxis model. Zbl 1163.37383Wang, Zhian; Hillen, Thomas 71 2007 \(M^5\) mesoscopic and macroscopic models for mesenchymal motion. Zbl 1112.92003Hillen, Thomas 62 2006 The one-dimensional chemotaxis model: global existence and asymptotic profile. Zbl 1081.92005Hillen, Thomas; Potapov, Alex 55 2004 Shock formation in a chemotaxis model. Zbl 1147.35057Wang, Zhian; Hillen, Thomas 50 2008 Mathematical modelling of glioma growth: the use of diffusion tensor imaging (DTI) data to predict the anisotropic pathways of cancer invasion. Zbl 1314.92083Painter, K. J.; Hillen, T. 49 2013 Hyperbolic models for chemosensitive movement. Zbl 1163.35491Hillen, Thomas 49 2002 Global existence for chemotaxis with finite sampling radius. Zbl 1116.92011Hillen, T.; Painter, K.; Schmeiser, C. 45 2007 Glioma follow white matter tracts: a multiscale DTI-based model. Zbl 1343.92072Engwer, Christian; Hillen, Thomas; Knappitsch, Markus; Surulescu, Christina 40 2015 Metastability in chemotaxis models. Zbl 1170.35460Potapov, A. B.; Hillen, T. 35 2005 Continuous traveling waves for prey-taxis. Zbl 1142.92043Lee, J. M.; Hillen, T.; Lewis, M. A. 33 2008 Transport and anisotropic diffusion models for movement in oriented habitats. Zbl 1347.92065Hillen, Thomas; Painter, Kevin J. 33 2013 Hyperbolic models for chemotaxis in 1-D. Zbl 0981.92003Hillen, T.; Stevens, A. 33 2000 Modeling cell movement in anisotropic and heterogeneous network tissues. Zbl 1115.92009Chauviere, A.; Hillen, T.; Preziosi, L. 32 2007 A Turing model with correlated random walk. Zbl 0863.92001Hillen, Thomas 29 1996 The tumor growth paradox and immune system-mediated selection for cancer stem cells. Zbl 1272.92026Hillen, Thomas; Enderling, Heiko; Hahnfeldt, Philip 27 2013 Transport equations with resting phases. Zbl 1050.92052Hillen, T. 24 2003 A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis. Zbl 1392.92012Buttenschön, Andreas; Hillen, Thomas; Gerisch, Alf; Painter, Kevin J. 22 2018 A course in mathematical biology. Quantitative modeling with mathematical and computational methods. Zbl 1105.92002de Vries, Gerda; Hillen, Thomas; Lewis, Mark; Müller, Johannes; Schönfisch, Birgitt 22 2006 Cattaneo models for chemosensitive movement. Zbl 1020.92004Dolak, Y.; Hillen, T. 18 2003 The Langevin or Kramers approach to biological modeling. Zbl 1057.92012Hadeler, Karl P.; Hillen, Thomas; Lutscher, Frithjof 17 2004 Hyperbolic systems and transport equations in mathematical biology. Zbl 1087.92002Hillen, T.; Hadeler, K. P. 16 2005 Existence of weak solutions for a hyperbolic model of chemosensitive movement. Zbl 0984.35043Hillen, Thomas; Rohde, Christian; Lutscher, Frithjof 16 2001 Mathematical analysis of a kinetic model for cell movement in network tissues. Zbl 1205.35165Hillen, Thomas; Hinow, Peter; Wang, Zhi-An 15 2010 Existence theory for correlated random walks on bounded domains. Zbl 1201.35127Hillen, T. 14 2010 Erratum: Cattaneo models for chemosensitive movement. Numerical solution and pattern formation. Zbl 1062.92501Dolak, Y.; Hillen, T. 14 2003 Anisotropic diffusion in oriented environments can lead to singularity formation. Zbl 1273.35165Hillen, Thomas; Painter, Kevin J.; Winkler, Michael 13 2013 A patient-specific anisotropic diffusion model for brain tumour spread. Zbl 1394.92064Swan, Amanda; Hillen, Thomas; Bowman, John C.; Murtha, Albert D. 13 2018 Qualitative analysis of semilinear Cattaneo equations. Zbl 0911.35023Hillen, T. 13 1998 Derivation of the tumour control probability (TCP) from a cell cycle model. Zbl 1111.92029Dawson, A.; Hillen, T. 12 2006 Invariance principles for hyperbolic random walk systems. Zbl 0880.60030Hillen, Thomas 12 1997 On the \(L^2\)-moment closure of transport equations: The Cattaneo approximation. Zbl 1052.92006Hillen, T. 11 2004 On the \(L^2\)-moment closure of transport equations: the general case. Zbl 1077.92004Hillen, T. 11 2005 Biological modeling with quiescent phases. Zbl 1179.92001Hadeler, Karl P.; Hillen, Thomas; Lewis, Mark A. 10 2010 Linear quadratic and tumour control probability modelling in external beam radiotherapy. Zbl 1311.92105O’Rourke, S. F. C.; McAneney, H.; Hillen, T. 10 2009 A mathematical model for \(M\)-phase specific chemotherapy including the \(G_0\)-phase and immunoresponse. Zbl 1123.92014Liu, Wenxiang; Hillen, Thomas; Freedman, H. I. 10 2007 The diffusion limit of transport equations in biology. Zbl 1353.92077Hillen, Thomas; Swan, Amanda 9 2016 Coupled dynamics and quiescent phases. Zbl 1127.37025Hadeler, Karl P.; Hillen, Thomas 9 2007 A non-local model for cancer stem cells and the tumour growth paradox. Zbl 1400.92244Borsi, I.; Fasano, A.; Primicerio, M.; Hillen, T. 9 2017 Global solvability and explicit bounds for non-local adhesion models. Zbl 1406.35430Hillen, T.; Painter, K. J.; Winkler, M. 9 2018 Feedback regulation in a cancer stem cell model can cause an Allee effect. Zbl 1341.92029Konstorum, Anna; Hillen, Thomas; Lowengrub, John 9 2016 Nonlocal adhesion models for microorganisms on bounded domains. Zbl 1433.92012Hillen, Thomas; Buttenschön, Andreas 9 2020 Are more complicated tumour control probability models better? Zbl 1318.92029Gong, Jiafen; Dos Santos, Mairon M.; Finlay, Chris; Hillen, Thomas 8 2013 Moments of von Mises and Fisher distributions and applications. Zbl 1358.35204Hillen, Thomas; Painter, Kevin J.; Swan, Amanda C.; Murtha, Albert D. 7 2017 The effect of wind on the propagation of an idealized forest fire. Zbl 1194.92070Babak, Petro; Bourlioux, Anne; Hillen, Thomas 7 2009 Modeling the motion of a cell population in the extracellular matrix. Zbl 1163.92313Chauviere, A.; Preziosi, L.; Hillen, T. 7 2007 A classification of spikes and plateaus. Zbl 1160.35033Hillen, Thomas 7 2007 Spatial dynamics in ecology. Zbl 1352.92179Lewis, Mark A.; Hillen, Thomas; Lutscher, Frithjof 6 2009 Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model. Zbl 1301.92005Hillen, Thomas; Zielinski, Jeffery; Painter, Kevin J. 6 2013 Partial differential equations. Theory and completely solved problems. Zbl 1280.35001Hillen, Thomas; Leonard, I. Ed; van Roessel, Henry 6 2012 A reaction-diffusion model for radiation-induced bystander effects. Zbl 1377.92026Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas 5 2017 Blow-up and pattern formation in hyperbolic models for chemotaxis in 1-D. Zbl 1030.92005Hillen, T.; Levine, H. A. 5 2003 Mesenchymal motion models in one dimension. Zbl 1183.35196Wang, Zhi-An; Hillen, Thomas; Li, Michael 4 2008 Nonlinear hyperbolic systems for modeling propagations and application to the Turing model. (Nichtlineare hyperbolische Systeme zur Modellierung von Ausbreitungsvorgängen und Anwendung auf das Turing Modell.) Zbl 0878.35071Hillen, Thomas 4 1995 Birth-jump processes and application to forest fire spotting. Zbl 1448.92374Hillen, T.; Greese, B.; Martin, J.; de Vries, G. 4 2015 Mathematical modeling of the role of survivin on dedifferentiation and radioresistance in cancer. Zbl 1348.92086Rhodes, Adam; Hillen, Thomas 4 2016 Local and global existence for nonlocal multispecies advection-diffusion models. Zbl 1494.35002Giunta, Valeria; Hillen, Thomas; Lewis, Mark; Potts, Jonathan R. 4 2022 Modulation equations and parabolic limits of reaction random-walk systems. Zbl 0909.35015Müller, Johannes; Hillen, Thomas 4 1998 Non-local cell adhesion models. Symmetries and bifurcations in 1-D. Zbl 1473.92001Buttenschön, Andreas; Hillen, Thomas 4 2021 A mathematical model for the immune-mediated theory of metastasis. Zbl 1422.92031Rhodes, Adam; Hillen, Thomas 3 2019 Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment. Zbl 1451.92106Rhodes, Adam; Hillen, Thomas 3 2020 Homogenization of a reaction diffusion equation can explain influenza a virus load data. Zbl 1470.92280Baabdulla, Arwa Abdulla; Now, Hesung; Park, Ju An; Kim, Woo-Jong; Jung, Sungjune; Yoo, Joo-Yeon; Hillen, Thomas 1 2021 Differential equations on branched manifolds. Zbl 0797.58071Hadeler, K. P.; Hillen, Thomas 1 1993 Burning issues with Prometheus – the Canadian wildland fire growth simulation model. Zbl 1201.80069Barber, J.; Bose, C.; Bourlioux, A.; Braun, J.; Brunelle, E.; Garcia, T.; Hillen, T.; Ong, B. 1 2008 Effects of G2-checkpoint dynamics on low-dose hyper-radiosensitivity. Zbl 1404.92101Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas 1 2018 A stochastic model for the normal tissue complication probability (NTCP) and applicationss. Zbl 1400.92289Stocks, Theresa; Hillen, Thomas; Gong, Jiafen; Burger, Martin 1 2017 Correlated random walks in heterogeneous landscapes: derivation, homogenization, and invasion fronts. Zbl 1485.35028Lutscher, Frithjof; Hillen, Thomas 1 2021 A stochastic model for cancer metastasis: branching stochastic process with settlement. Zbl 1504.92034Frei, Christoph; Hillen, Thomas; Rhodes, Adam 1 2020 Local and global existence for nonlocal multispecies advection-diffusion models. Zbl 1494.35002Giunta, Valeria; Hillen, Thomas; Lewis, Mark; Potts, Jonathan R. 4 2022 Non-local cell adhesion models. Symmetries and bifurcations in 1-D. Zbl 1473.92001Buttenschön, Andreas; Hillen, Thomas 4 2021 Homogenization of a reaction diffusion equation can explain influenza a virus load data. Zbl 1470.92280Baabdulla, Arwa Abdulla; Now, Hesung; Park, Ju An; Kim, Woo-Jong; Jung, Sungjune; Yoo, Joo-Yeon; Hillen, Thomas 1 2021 Correlated random walks in heterogeneous landscapes: derivation, homogenization, and invasion fronts. Zbl 1485.35028Lutscher, Frithjof; Hillen, Thomas 1 2021 Nonlocal adhesion models for microorganisms on bounded domains. Zbl 1433.92012Hillen, Thomas; Buttenschön, Andreas 9 2020 Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment. Zbl 1451.92106Rhodes, Adam; Hillen, Thomas 3 2020 A stochastic model for cancer metastasis: branching stochastic process with settlement. Zbl 1504.92034Frei, Christoph; Hillen, Thomas; Rhodes, Adam 1 2020 A mathematical model for the immune-mediated theory of metastasis. Zbl 1422.92031Rhodes, Adam; Hillen, Thomas 3 2019 A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis. Zbl 1392.92012Buttenschön, Andreas; Hillen, Thomas; Gerisch, Alf; Painter, Kevin J. 22 2018 A patient-specific anisotropic diffusion model for brain tumour spread. Zbl 1394.92064Swan, Amanda; Hillen, Thomas; Bowman, John C.; Murtha, Albert D. 13 2018 Global solvability and explicit bounds for non-local adhesion models. Zbl 1406.35430Hillen, T.; Painter, K. J.; Winkler, M. 9 2018 Effects of G2-checkpoint dynamics on low-dose hyper-radiosensitivity. Zbl 1404.92101Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas 1 2018 A non-local model for cancer stem cells and the tumour growth paradox. Zbl 1400.92244Borsi, I.; Fasano, A.; Primicerio, M.; Hillen, T. 9 2017 Moments of von Mises and Fisher distributions and applications. Zbl 1358.35204Hillen, Thomas; Painter, Kevin J.; Swan, Amanda C.; Murtha, Albert D. 7 2017 A reaction-diffusion model for radiation-induced bystander effects. Zbl 1377.92026Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas 5 2017 A stochastic model for the normal tissue complication probability (NTCP) and applicationss. Zbl 1400.92289Stocks, Theresa; Hillen, Thomas; Gong, Jiafen; Burger, Martin 1 2017 The diffusion limit of transport equations in biology. Zbl 1353.92077Hillen, Thomas; Swan, Amanda 9 2016 Feedback regulation in a cancer stem cell model can cause an Allee effect. Zbl 1341.92029Konstorum, Anna; Hillen, Thomas; Lowengrub, John 9 2016 Mathematical modeling of the role of survivin on dedifferentiation and radioresistance in cancer. Zbl 1348.92086Rhodes, Adam; Hillen, Thomas 4 2016 Glioma follow white matter tracts: a multiscale DTI-based model. Zbl 1343.92072Engwer, Christian; Hillen, Thomas; Knappitsch, Markus; Surulescu, Christina 40 2015 Birth-jump processes and application to forest fire spotting. Zbl 1448.92374Hillen, T.; Greese, B.; Martin, J.; de Vries, G. 4 2015 Convergence of a cancer invasion model to a logistic chemotaxis model. Zbl 1263.35204Hillen, Thomas; Painter, Kevin J.; Winkler, Michael 83 2013 Mathematical modelling of glioma growth: the use of diffusion tensor imaging (DTI) data to predict the anisotropic pathways of cancer invasion. Zbl 1314.92083Painter, K. J.; Hillen, T. 49 2013 Transport and anisotropic diffusion models for movement in oriented habitats. Zbl 1347.92065Hillen, Thomas; Painter, Kevin J. 33 2013 The tumor growth paradox and immune system-mediated selection for cancer stem cells. Zbl 1272.92026Hillen, Thomas; Enderling, Heiko; Hahnfeldt, Philip 27 2013 Anisotropic diffusion in oriented environments can lead to singularity formation. Zbl 1273.35165Hillen, Thomas; Painter, Kevin J.; Winkler, Michael 13 2013 Are more complicated tumour control probability models better? Zbl 1318.92029Gong, Jiafen; Dos Santos, Mairon M.; Finlay, Chris; Hillen, Thomas 8 2013 Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model. Zbl 1301.92005Hillen, Thomas; Zielinski, Jeffery; Painter, Kevin J. 6 2013 Partial differential equations. Theory and completely solved problems. Zbl 1280.35001Hillen, Thomas; Leonard, I. Ed; van Roessel, Henry 6 2012 Spatio-temporal chaos in a chemotaxis model. Zbl 1255.37026Painter, Kevin J.; Hillen, Thomas 114 2011 Mathematical analysis of a kinetic model for cell movement in network tissues. Zbl 1205.35165Hillen, Thomas; Hinow, Peter; Wang, Zhi-An 15 2010 Existence theory for correlated random walks on bounded domains. Zbl 1201.35127Hillen, T. 14 2010 Biological modeling with quiescent phases. Zbl 1179.92001Hadeler, Karl P.; Hillen, Thomas; Lewis, Mark A. 10 2010 A user’s guide to PDE models for chemotaxis. Zbl 1161.92003Hillen, T.; Painter, K. J. 844 2009 Pattern formation in prey-taxis systems. Zbl 1315.92064Lee, J. M.; Hillen, T.; Lewis, M. A. 90 2009 Linear quadratic and tumour control probability modelling in external beam radiotherapy. Zbl 1311.92105O’Rourke, S. F. C.; McAneney, H.; Hillen, T. 10 2009 The effect of wind on the propagation of an idealized forest fire. Zbl 1194.92070Babak, Petro; Bourlioux, Anne; Hillen, Thomas 7 2009 Spatial dynamics in ecology. Zbl 1352.92179Lewis, Mark A.; Hillen, Thomas; Lutscher, Frithjof 6 2009 Shock formation in a chemotaxis model. Zbl 1147.35057Wang, Zhian; Hillen, Thomas 50 2008 Continuous traveling waves for prey-taxis. Zbl 1142.92043Lee, J. M.; Hillen, T.; Lewis, M. A. 33 2008 Mesenchymal motion models in one dimension. Zbl 1183.35196Wang, Zhi-An; Hillen, Thomas; Li, Michael 4 2008 Burning issues with Prometheus – the Canadian wildland fire growth simulation model. Zbl 1201.80069Barber, J.; Bose, C.; Bourlioux, A.; Braun, J.; Brunelle, E.; Garcia, T.; Hillen, T.; Ong, B. 1 2008 Classical solutions and pattern formation for a volume filling chemotaxis model. Zbl 1163.37383Wang, Zhian; Hillen, Thomas 71 2007 Global existence for chemotaxis with finite sampling radius. Zbl 1116.92011Hillen, T.; Painter, K.; Schmeiser, C. 45 2007 Modeling cell movement in anisotropic and heterogeneous network tissues. Zbl 1115.92009Chauviere, A.; Hillen, T.; Preziosi, L. 32 2007 A mathematical model for \(M\)-phase specific chemotherapy including the \(G_0\)-phase and immunoresponse. Zbl 1123.92014Liu, Wenxiang; Hillen, Thomas; Freedman, H. I. 10 2007 Coupled dynamics and quiescent phases. Zbl 1127.37025Hadeler, Karl P.; Hillen, Thomas 9 2007 Modeling the motion of a cell population in the extracellular matrix. Zbl 1163.92313Chauviere, A.; Preziosi, L.; Hillen, T. 7 2007 A classification of spikes and plateaus. Zbl 1160.35033Hillen, Thomas 7 2007 \(M^5\) mesoscopic and macroscopic models for mesenchymal motion. Zbl 1112.92003Hillen, Thomas 62 2006 A course in mathematical biology. Quantitative modeling with mathematical and computational methods. Zbl 1105.92002de Vries, Gerda; Hillen, Thomas; Lewis, Mark; Müller, Johannes; Schönfisch, Birgitt 22 2006 Derivation of the tumour control probability (TCP) from a cell cycle model. Zbl 1111.92029Dawson, A.; Hillen, T. 12 2006 Metastability in chemotaxis models. Zbl 1170.35460Potapov, A. B.; Hillen, T. 35 2005 Hyperbolic systems and transport equations in mathematical biology. Zbl 1087.92002Hillen, T.; Hadeler, K. P. 16 2005 On the \(L^2\)-moment closure of transport equations: the general case. Zbl 1077.92004Hillen, T. 11 2005 The one-dimensional chemotaxis model: global existence and asymptotic profile. Zbl 1081.92005Hillen, Thomas; Potapov, Alex 55 2004 The Langevin or Kramers approach to biological modeling. Zbl 1057.92012Hadeler, Karl P.; Hillen, Thomas; Lutscher, Frithjof 17 2004 On the \(L^2\)-moment closure of transport equations: The Cattaneo approximation. Zbl 1052.92006Hillen, T. 11 2004 Transport equations with resting phases. Zbl 1050.92052Hillen, T. 24 2003 Cattaneo models for chemosensitive movement. Zbl 1020.92004Dolak, Y.; Hillen, T. 18 2003 Erratum: Cattaneo models for chemosensitive movement. Numerical solution and pattern formation. Zbl 1062.92501Dolak, Y.; Hillen, T. 14 2003 Blow-up and pattern formation in hyperbolic models for chemotaxis in 1-D. Zbl 1030.92005Hillen, T.; Levine, H. A. 5 2003 Volume-filling and quorum-sensing in models for chemosensitive movement. Zbl 1057.92013Painter, Kevin J.; Hillen, Thomas 330 2002 The diffusion limit of transport equations. II: Chemotaxis equations. Zbl 1103.35098Othmer, Hans G.; Hillen, Thomas 169 2002 Hyperbolic models for chemosensitive movement. Zbl 1163.35491Hillen, Thomas 49 2002 Global existence for a parabolic chemotaxis model with prevention of overcrowding. Zbl 0998.92006Hillen, T.; Painter, K. 160 2001 Existence of weak solutions for a hyperbolic model of chemosensitive movement. Zbl 0984.35043Hillen, Thomas; Rohde, Christian; Lutscher, Frithjof 16 2001 The diffusion limit of transport equations derived from velocity-jump processes. Zbl 1002.35120Hillen, Thomas; Othmer, Hans G. 155 2000 Hyperbolic models for chemotaxis in 1-D. Zbl 0981.92003Hillen, T.; Stevens, A. 33 2000 Qualitative analysis of semilinear Cattaneo equations. Zbl 0911.35023Hillen, T. 13 1998 Modulation equations and parabolic limits of reaction random-walk systems. Zbl 0909.35015Müller, Johannes; Hillen, Thomas 4 1998 Invariance principles for hyperbolic random walk systems. Zbl 0880.60030Hillen, Thomas 12 1997 A Turing model with correlated random walk. Zbl 0863.92001Hillen, Thomas 29 1996 Nonlinear hyperbolic systems for modeling propagations and application to the Turing model. (Nichtlineare hyperbolische Systeme zur Modellierung von Ausbreitungsvorgängen und Anwendung auf das Turing Modell.) Zbl 0878.35071Hillen, Thomas 4 1995 Differential equations on branched manifolds. Zbl 0797.58071Hadeler, K. P.; Hillen, Thomas 1 1993 all cited Publications top 5 cited Publications all top 5 Cited by 2,052 Authors 94 Winkler, Michael 44 Mu, Chunlai 44 Wang, Zhian 42 Hillen, Thomas 37 Tao, Youshan 37 Zheng, Jiashan 32 Bellomo, Nicola 30 Painter, Kevin J. 28 Yokota, Tomomi 27 Zheng, Pan 25 Surulescu, Christina 22 Jin, Haiyang 22 Wang, Liangchen 21 Carrillo de la Plata, José Antonio 21 Wang, Yifu 19 Liu, Bin 18 Wang, Qi 17 Xiang, Tian 16 Perthame, Benoît 16 Ren, Guoqiang 16 Zheng, Sining 15 Calvez, Vincent 14 Lankeit, Johannes 14 Shen, Wenxian 13 Bellouquid, Abdelghani 13 Chaplain, Mark A. J. 13 Lin, Ke 12 Cao, Xinru 12 Ma, Manjun 12 Mizukami, Masaaki 12 Soler, Juan S. 11 Black, Tobias 11 Fujie, Kentaro 11 Kim, Yongjung 11 Stinner, Christian 11 Vauchelet, Nicolas 11 Wang, Yilong 10 Bressloff, Paul C. 10 Fuest, Mario 10 Hadeler, Karl-Peter 10 Ke, Yuanyuan 10 Lewis, Mark Alun 10 Li, Tong 10 Li, Yuxiang 10 Maini, Philip Kumar 10 Xiang, Zhaoyin 10 Zhao, Kun 9 Dai, Feng 9 de Vries, Gerda 9 Eftimie, Raluca 9 Fu, Shengmao 9 Ishida, Sachiko 9 Liu, Ji 9 Lorenzi, Tommaso 9 Saad, Mazen 9 Trucu, Dumitru 8 Delitala, Marcello Edoardo 8 Gerisch, Alf 8 Granero Belinchón, Rafael 8 Li, Dan 8 Li, Xie 8 Liu, Zhengrong 8 Qiu, Shuyan 8 Shi, Junping 8 Wang, Jinfeng 8 Wang, Wei 8 Wu, Sainan 7 Boccardo, Lucio 7 Byrne, Helen Mary 7 Chen, Xinfu 7 Guo, Shangjiang 7 Hu, Xuegang 7 Jüngel, Ansgar 7 Klar, Axel 7 Kmit, Irina 7 Li, Jing 7 Li, Yan 7 Liu, Zuhan 7 Lutscher, Frithjof 7 Lv, Wenbin 7 Lyu, Wenbin 7 Nieto, Juanjo 7 Scheel, Arnd 7 Sherratt, Jonathan A. 7 Viglialoro, Giuseppe 7 Wang, Jianping 7 Wang, Yulan 7 Xue, Chuan 6 Bianca, Carlo 6 Chamoun, Georges 6 Chiyo, Yutaro 6 Enderling, Heiko 6 Gosse, Laurent 6 Han, Yazhou 6 Issa, Tahir Bachar 6 Jiang, Jie 6 Kolbe, Niklas 6 Kong, Fanze 6 Kurganov, Alexander 6 Li, Zhongping ...and 1,952 more Authors all top 5 Cited in 248 Serials 141 Journal of Differential Equations 114 Journal of Mathematical Analysis and Applications 109 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 92 Journal of Mathematical Biology 82 Discrete and Continuous Dynamical Systems. Series B 66 Nonlinear Analysis. Real World Applications 65 Bulletin of Mathematical Biology 60 Journal of Theoretical Biology 54 ZAMP. Zeitschrift für angewandte Mathematik und Physik 45 Discrete and Continuous Dynamical Systems 41 Computers & Mathematics with Applications 34 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Mathematical Methods in the Applied Sciences 26 Applied Mathematics Letters 25 Nonlinearity 24 Mathematical Biosciences and Engineering 22 SIAM Journal on Applied Mathematics 19 Physica D 19 Mathematical and Computer Modelling 19 Communications on Pure and Applied Analysis 18 Applicable Analysis 18 Mathematical Biosciences 18 Acta Applicandae Mathematicae 18 Kinetic and Related Models 16 SIAM Journal on Mathematical Analysis 16 Journal of Dynamics and Differential Equations 15 European Journal of Applied Mathematics 15 Journal of Biological Dynamics 13 Journal of Computational Physics 13 Discrete and Continuous Dynamical Systems. Series S 12 Journal of Mathematical Physics 11 Applied Mathematics and Computation 11 Communications in Partial Differential Equations 11 Mathematical Modelling of Natural Phenomena 10 Physica A 9 Journal of Nonlinear Science 9 Calculus of Variations and Partial Differential Equations 9 NoDEA. Nonlinear Differential Equations and Applications 9 Multiscale Modeling & Simulation 8 Communications in Nonlinear Science and Numerical Simulation 8 Journal of Evolution Equations 8 Boundary Value Problems 7 Chaos, Solitons and Fractals 7 Applied Mathematical Modelling 7 International Journal of Biomathematics 6 Mathematics and Computers in Simulation 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Applied Numerical Mathematics 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Networks and Heterogeneous Media 5 Indiana University Mathematics Journal 5 Ricerche di Matematica 5 Journal of Scientific Computing 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 SIAM Journal on Scientific Computing 5 Electronic Journal of Differential Equations (EJDE) 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 SIAM Journal on Applied Dynamical Systems 5 Journal of Statistical Mechanics: Theory and Experiment 5 Journal of Physics A: Mathematical and Theoretical 4 Archive for Rational Mechanics and Analysis 4 Applied Mathematics and Optimization 4 Journal of Computational and Applied Mathematics 4 Journal of Functional Analysis 4 Mathematische Nachrichten 4 Acta Mathematicae Applicatae Sinica. English Series 4 Japan Journal of Industrial and Applied Mathematics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Applied Mathematics. Series B (English Edition) 4 Abstract and Applied Analysis 4 Chaos 4 Advanced Nonlinear Studies 4 Nonlinear Analysis. Hybrid Systems 4 Science China. Mathematics 4 Advances in Nonlinear Analysis 4 SN Partial Differential Equations and Applications 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Statistical Physics 3 Numerische Mathematik 3 Proceedings of the American Mathematical Society 3 Quarterly of Applied Mathematics 3 Transactions of the American Mathematical Society 3 Statistics & Probability Letters 3 Applications of Mathematics 3 Engineering Analysis with Boundary Elements 3 Nonlinear Dynamics 3 Discrete Dynamics in Nature and Society 3 Journal of Biological Systems 3 Advances in Difference Equations 3 Oberwolfach Reports 3 Evolution Equations and Control Theory 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 AIMS Mathematics 3 Electronic Research Archive 2 International Journal of Modern Physics B 2 Computers and Fluids 2 Transport Theory and Statistical Physics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Bulletin of the London Mathematical Society ...and 148 more Serials all top 5 Cited in 36 Fields 1,485 Biology and other natural sciences (92-XX) 1,461 Partial differential equations (35-XX) 173 Numerical analysis (65-XX) 101 Probability theory and stochastic processes (60-XX) 86 Fluid mechanics (76-XX) 74 Statistical mechanics, structure of matter (82-XX) 65 Ordinary differential equations (34-XX) 46 Dynamical systems and ergodic theory (37-XX) 34 Integral equations (45-XX) 32 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 24 Operator theory (47-XX) 24 Systems theory; control (93-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 Classical thermodynamics, heat transfer (80-XX) 15 Mechanics of deformable solids (74-XX) 13 Operations research, mathematical programming (90-XX) 12 Computer science (68-XX) 11 Statistics (62-XX) 8 Functional analysis (46-XX) 6 General and overarching topics; collections (00-XX) 5 Real functions (26-XX) 5 Difference and functional equations (39-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) Citations by Year