Edit Profile (opens in new tab) Tao, Youshan Co-Author Distance Author ID: tao.youshan Published as: Tao, Youshan; Tao, Y.; Tao, You Shan; Tao, YouShan more...less Documents Indexed: 112 Publications since 1994, including 2 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 41 Co-Authors with 96 Joint Publications 2,127 Co-Co-Authors all top 5 Co-Authors 15 single-authored 43 Winkler, Michael 10 Guo, Qian 6 Bellomo, Nicola 4 Aihara, Kazuyuki 4 Gao, Guozhu 3 Li, Genglin 3 Lou, Yuan 3 Yi, Fahuai 3 Yoshida, Norio 2 Friedman, Avner 2 Hu, Bingran 2 Liu, Dongmei 2 Liu, Yuanyuan 2 Wang, Mingjun 2 Wang, Zhian 1 Bellouquid, Abdelghani 1 Bian, Baojun 1 Cao, Xinru 1 Chen, Miaojun 1 Chen, Zhen 1 Cui, Chun 1 Ding, Shijin 1 Fokas, Athanassios S. 1 He, Jingsong 1 Hong, Jiaxing 1 Hu, Bei 1 Jiang, Lishang 1 Li, Huayin 1 Liu, Zuhan 1 Outada, Nisrine 1 Painter, Kevin J. 1 Porsezian, Kuppusamy 1 Soler, Juan S. 1 Tang, Xifeng 1 Vernier-Piro, Stella 1 Wang, Lihe 1 Xu, Danni 1 Yang, Yan 1 Yin, Hongming 1 Zhang, Hongyi 1 Zhang, Hui 1 Zhang, Jizhou 1 Zhang, Na 1 Zhu, Guo all top 5 Serials 13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 10 Journal of Differential Equations 9 Journal of Mathematical Analysis and Applications 6 SIAM Journal on Mathematical Analysis 5 Applied Mathematics. Series B (English Edition) 5 Nonlinear Analysis. Real World Applications 5 Discrete and Continuous Dynamical Systems. Series B 4 Nonlinearity 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Journal of Mathematical Biology 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Applied Mathematics Letters 2 Science in China. Series A 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Partial Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Acta Mathematica Scientia. Series A. (Chinese Edition) 2 Applied Mathematical Sciences (Ruse) 1 Indian Journal of Pure & Applied Mathematics 1 Inverse Problems 1 Mathematical Methods in the Applied Sciences 1 Applied Mathematics and Computation 1 Journal of Functional Analysis 1 Proceedings of the London Mathematical Society. Third Series 1 Journal of Mathematics. Wuhan University 1 Journal of Mathematical Research & Exposition 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 European Journal of Applied Mathematics 1 SIAM Journal on Applied Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 The Canadian Applied Mathematics Quarterly 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Far East Journal of Applied Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Nonlinear Mathematical Physics 1 Basic Sciences Journal of Textile Universities 1 Communications on Pure and Applied Analysis 1 Communications in Mathematical Sciences 1 Mathematical Biosciences and Engineering 1 Toyama Mathematical Journal 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Discrete and Continuous Dynamical Systems. Series S 1 Evolution Equations and Control Theory all top 5 Fields 104 Partial differential equations (35-XX) 87 Biology and other natural sciences (92-XX) 4 Ordinary differential equations (34-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 93 Publications have been cited 4,671 times in 1,738 Documents Cited by ▼ Year ▼ Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397 Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M. 645 2015 Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity. Zbl 1382.35127 Tao, Youshan; Winkler, Michael 499 2012 Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant. Zbl 1268.35016 Tao, Youshan; Winkler, Michael 228 2012 Competing effects of attraction vs. repulsion in chemotaxis. Zbl 1403.35136 Tao, Youshan; Wang, Zhi-An 207 2013 Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154 Tao, Youshan; Winkler, Michael 170 2013 A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210 Tao, Youshan; Winkler, Michael 156 2011 Boundedness in a chemotaxis model with oxygen consumption by bacteria. Zbl 1225.35118 Tao, Youshan 154 2011 Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084 Tao, Youshan; Winkler, Michael 152 2015 Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105 Tao, Youshan; Winkler, Michael 148 2012 Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103 Tao, Youshan; Winkler, Michael 132 2015 Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant. Zbl 1295.35144 Tao, Youshan; Winkler, Michael 116 2014 Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis. Zbl 1195.35171 Tao, Youshan 112 2010 Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054 Tao, Youshan; Winkler, Michael 109 2016 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068 Tao, Youshan; Winkler, Michael 94 2017 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 1516.35092 Tao, Youshan; Winkler, Michael 87 2017 Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075 Winkler, Michael; Tao, Youshan 78 2015 Global solution for a chemotactic-haptotactic model of cancer invasion. Zbl 1160.35431 Tao, Youshan; Wang, Mingjun 69 2008 Global boundedness in a fully parabolic attraction-repulsion chemotaxis model. Zbl 1331.35174 Liu, Dongmei; Tao, Youshan 66 2015 To the exclusion of blow-up in a three-dimensional chemotaxis-growth model with indirect attractant production. Zbl 1351.35076 Hu, Bingran; Tao, Y. 66 2016 Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047 Tao, Youshan; Winkler, Michael 65 2014 A combined chemotaxis-haptotaxis system: the role of logistic source. Zbl 1201.35005 Tao, Youshan; Wang, Mingjun 63 2009 Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171 Tao, Youshan; Winkler, Michael 62 2014 Identifying the volatility of underlying assets from option prices. Zbl 0997.91024 Jiang, Lishang; Tao, Youshan 59 2001 Global existence for a haptotaxis model of cancer invasion with tissue remodeling. Zbl 1205.35144 Tao, Youshan 59 2011 Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source. Zbl 1160.92027 Tao, Youshan 55 2009 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615 Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael 54 2019 Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension. Zbl 1272.35040 Tao, Youshan; Wang, Lihe; Wang, Zhi-An 54 2013 Boundedness in a chemotaxis system with nonlinear signal production. Zbl 1374.35009 Liu, Dongmei; Tao, Youshan 52 2016 Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084 Tao, Youshan; Winkler, Michael 51 2015 Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039 Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M. 42 2022 Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity. Zbl 1282.35189 Tao, Youshan 39 2013 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200 Tao, Youshan; Winkler, Michael 37 2019 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132 Tao, Youshan; Winkler, Michael 37 2020 Stabilization in a chemotaxis model for virus infection. Zbl 1439.35052 Bellomo, Nicola; Tao, Youshan 36 2020 Boundedness in a parabolic-elliptic chemotaxis-growth system under a critical parameter condition. Zbl 1524.92020 Hu, Bingran; Tao, Youshan 34 2017 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480 Tao, Youshan; Winkler, Michael 31 2020 Boundedness in a chemotaxis system with indirect signal production and generalized logistic source. Zbl 1503.92021 Li, Huayin; Tao, Youshan 30 2018 An elliptic-hyperbolic free boundary problem modelling cancer therapy. Zbl 1105.35149 Tao, Youshan; Chen, Miaojun 23 2006 Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098 Lou, Yuan; Tao, Youshan; Winkler, Michael 22 2014 Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250 Li, Genglin; Tao, Youshan; Winkler, Michael 21 2020 A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181 Tao, Youshan; Winkler, Michael 21 2019 Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076 Tao, Youshan; Winkler, Michael 21 2021 A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation. Zbl 1471.35278 Tao, Youshan; Winkler, Michael 20 2021 The competitive dynamics between tumor cells, a replication-competent virus and an immune response. Zbl 1066.92035 Tao, Youshan; Guo, Qian 19 2005 Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146 Tao, Youshan; Winkler, Michael 19 2019 A free boundary problem modeling the cell cycle and cell movement in multicellular tumor spheroids. Zbl 1178.35387 Tao, Youshan 18 2009 Nonlinear stability of the Muskat problem with capillary pressure at the free boundary. Zbl 1028.35123 Friedman, Avner; Tao, Youshan 18 2003 Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Zbl 1479.35120 Tao, Youshan; Winkler, Michael 18 2021 Analysis of a model of a virus that replicates selectively in tumor cells. Zbl 1052.92027 Friedman, Avner; Tao, Youshan 17 2003 Boundedness and stabilization enforced by mild saturation of taxis in a producer-scrounger model. Zbl 1459.92018 Cao, Xinru; Tao, Youshan 15 2021 Nonlinear analysis of a model of vascular tumour growth and treatment. Zbl 1073.35215 Tao, Youshan; Yoshida, Norio; Guo, Qian 14 2004 Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system. Zbl 1496.35228 Tao, Youshan; Winkler, Michael 14 2022 Rogue wave management in an inhomogeneous nonlinear fibre with higher order effects. Zbl 1420.35357 He, J. S.; Tao, Y. S.; Porsezian, K.; Fokas, A. S. 14 2013 A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus. Zbl 1115.35137 Tao, Youshan; Zhang, Hui 13 2007 Global solution to a model of tumor invasion. Zbl 1135.92020 Tao, Youshan; Zhu, Guo 13 2007 Taxis-driven formation of singular hotspots in a May-Nowak-type model for virus infection. Zbl 1461.35201 Tao, Youshan; Winkler, Michael 13 2021 A density-dependent chemotaxis-haptotaxis system modeling cancer invasion. Zbl 1186.92026 Tao, Youshan; Cui, Chun 12 2010 A critical virus production rate for efficiency of oncolytic virotherapy. Zbl 1526.92012 Tao, Youshan; Winkler, Michael 12 2021 Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model. Zbl 1372.35038 Lou, Yuan; Tao, Youshan; Winkler, Michael 11 2017 Muskat problem with surface tension. Zbl 0884.35176 Hong, Jiaxing; Tao, Youshan; Yi, Fahuai 10 1997 A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy. Zbl 1303.35116 Tao, Youshan; Guo, Qian; Aihara, Kazuyuki 10 2014 Mathematical modeling of prostate tumor growth under intermittent androgen suppression with partial differential equations. Zbl 1165.92309 Guo, Qian; Tao, Youshan; Aihara, Kazuyuki 10 2008 A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor. Zbl 1196.35216 Tao, Youshan; Guo, Qian; Aihara, Kazuyuki 10 2010 A model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression. Zbl 1180.35584 Tao, Youshan; Guo, Qian; Aihara, Kazuyuki 9 2009 Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275 Tao, Youshan; Winkler, Michael 9 2019 Analysis of a chemotaxis-convection model of capillary-sprout growth during tumor angiogenesis. Zbl 1439.35101 Li, Genglin; Tao, Youshan 9 2020 A free boundary problem modelling cancer radiovirotherapy. Zbl 1141.35476 Tao, Youshan; Guo, Qian 8 2007 Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Zbl 1505.35340 Tao, Youshan; Winkler, Michael 8 2023 Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. Zbl 1484.35363 Tao, Youshan; Winkler, Michael 8 2022 The role of local kinetics in a three-component chemotaxis model for Alopecia areata. Zbl 1481.35061 Lou, Yuan; Tao, Youshan 7 2021 Large-data solutions in a three-dimensional chemotaxis-haptotaxis system with remodeling of non-diffusible attractant: the role of sub-linear production of diffusible signal. Zbl 1423.35194 Chen, Zhen; Tao, Youshan 7 2019 Analysis of a chemotaxis model for multi-species host-parasitoid interactions. Zbl 1159.35376 Tang, Xifeng; Tao, Youshan 6 2008 Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion. Zbl 1326.35407 Tao, Youshan; Tello, J. Ignacio 6 2016 Explicit lower bound of blow-up time in a fully parabolic chemotaxis system with nonlinear cross-diffusion. Zbl 1331.35167 Tao, Youshan; Vernier Piro, Stella 6 2016 Asymptotic behavior in a chemotaxis-growth system with nonlinear production of signals. Zbl 1360.35028 Tao, Youshan; Liu, Yuanyuan 6 2017 Combined effects of nonlinear proliferation and logistic damping in a three-component chemotaxis system for alopecia areata. Zbl 1482.35232 Tao, Youshan; Xu, Danni 6 2022 Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. Zbl 1451.92062 Bellomo, N.; Tao, Y.; Winkler, M. 5 2020 Quasi-stationary Stefan problem as limit case of Mullins-Sekerka problem. Zbl 0883.35137 Yi, Fahuai; Tao, Youshan; Liu, Zuhan 4 1997 Existence, uniqueness and approximation of classical solutions to nonlinear two-point boundary value problems. Zbl 1011.34008 Tao, Youshan; Gao, Guozhu 3 2002 Cross-diffusion models: analytic and multiscale problems. Zbl 1408.35078 Bellomo, N.; Tao, Y.; Winkler, M. 3 2018 Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Zbl 1525.35038 Tao, Youshan; Winkler, Michael 3 2023 Dynamics in a parabolic-elliptic two-species population competition model with cross-diffusion for one species. Zbl 1480.92174 Liu, Yuanyuan; Tao, Youshan 2 2017 Oscillation of nonlinear hyperbolic equations with distributed deviating arguments. Zbl 1107.35405 Tao, Youshan; Yoshida, Norio 2 2005 Classical Verigin problem as a limit case of Verigin problem with surface tension at free boundary. Zbl 0859.35065 Tao, Youshan; Yi, Fahuai 2 1996 Classical solution of Verigin problem with surface tension. Zbl 0889.35055 Tao, Youshan 2 1997 Parameter identification for a model of tumor growth in the presence of inhibitors. Zbl 1212.35516 Tao, Youshan; Bian, Baojun 2 2009 Spin Hall effect associated with \(SU(2)\) gauge field. Zbl 1188.81101 Tao, Y. 1 2010 A chemical diffusion process with reaction taking place at free boundary. Zbl 0906.35117 Ding, Shijin; Tao, Youshan; Yin, Hong-Ming 1 1997 Parabolic approximation to variational problems with double obstacles. Zbl 0990.49012 Tao, Youshan; Gao, Guozhu 1 2001 Analysis and simulation of a model for intracellular drug accumulation in tumors. Zbl 1089.92027 Tao, Youshan; Guo, Qian 1 2006 Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Zbl 1518.35439 Tao, Youshan; Winkler, Michael 1 2023 The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. Zbl 1465.35378 Tao, Youshan; Winkler, Michael 1 2021 Critical mass of lymphocytes for the coexistence in a chemotaxis system modeling tumor-immune cell interactions. Zbl 1464.35364 Hu, Bei; Tao, Youshan 1 2020 Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Zbl 1505.35340 Tao, Youshan; Winkler, Michael 8 2023 Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. Zbl 1525.35038 Tao, Youshan; Winkler, Michael 3 2023 Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers. Zbl 1518.35439 Tao, Youshan; Winkler, Michael 1 2023 Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. Zbl 1497.35039 Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M. 42 2022 Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system. Zbl 1496.35228 Tao, Youshan; Winkler, Michael 14 2022 Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. Zbl 1484.35363 Tao, Youshan; Winkler, Michael 8 2022 Combined effects of nonlinear proliferation and logistic damping in a three-component chemotaxis system for alopecia areata. Zbl 1482.35232 Tao, Youshan; Xu, Danni 6 2022 Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Zbl 1458.35076 Tao, Youshan; Winkler, Michael 21 2021 A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation. Zbl 1471.35278 Tao, Youshan; Winkler, Michael 20 2021 Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Zbl 1479.35120 Tao, Youshan; Winkler, Michael 18 2021 Boundedness and stabilization enforced by mild saturation of taxis in a producer-scrounger model. Zbl 1459.92018 Cao, Xinru; Tao, Youshan 15 2021 Taxis-driven formation of singular hotspots in a May-Nowak-type model for virus infection. Zbl 1461.35201 Tao, Youshan; Winkler, Michael 13 2021 A critical virus production rate for efficiency of oncolytic virotherapy. Zbl 1526.92012 Tao, Youshan; Winkler, Michael 12 2021 The role of local kinetics in a three-component chemotaxis model for Alopecia areata. Zbl 1481.35061 Lou, Yuan; Tao, Youshan 7 2021 The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. Zbl 1465.35378 Tao, Youshan; Winkler, Michael 1 2021 Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy. Zbl 1430.35132 Tao, Youshan; Winkler, Michael 37 2020 Stabilization in a chemotaxis model for virus infection. Zbl 1439.35052 Bellomo, Nicola; Tao, Youshan 36 2020 A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. Zbl 1442.35480 Tao, Youshan; Winkler, Michael 31 2020 Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Zbl 1453.92250 Li, Genglin; Tao, Youshan; Winkler, Michael 21 2020 Analysis of a chemotaxis-convection model of capillary-sprout growth during tumor angiogenesis. Zbl 1439.35101 Li, Genglin; Tao, Youshan 9 2020 Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. Zbl 1451.92062 Bellomo, N.; Tao, Y.; Winkler, M. 5 2020 Critical mass of lymphocytes for the coexistence in a chemotaxis system modeling tumor-immune cell interactions. Zbl 1464.35364 Hu, Bei; Tao, Youshan 1 2020 Occurrence vs. absence of taxis-driven instabilities in a May-Nowak model for virus infection. Zbl 1428.35615 Bellomo, Nicola; Painter, Kevin J.; Tao, Youshan; Winkler, Michael 54 2019 Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food. Zbl 1425.35200 Tao, Youshan; Winkler, Michael 37 2019 A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production. Zbl 1412.35181 Tao, Youshan; Winkler, Michael 21 2019 Global smooth solvability of a parabolic-elliptic nutrient taxis system in domains of arbitrary dimension. Zbl 1411.35146 Tao, Youshan; Winkler, Michael 19 2019 Boundedness and stabilization in a population model with cross-diffusion for one species. Zbl 1439.35275 Tao, Youshan; Winkler, Michael 9 2019 Large-data solutions in a three-dimensional chemotaxis-haptotaxis system with remodeling of non-diffusible attractant: the role of sub-linear production of diffusible signal. Zbl 1423.35194 Chen, Zhen; Tao, Youshan 7 2019 Boundedness in a chemotaxis system with indirect signal production and generalized logistic source. Zbl 1503.92021 Li, Huayin; Tao, Youshan 30 2018 Cross-diffusion models: analytic and multiscale problems. Zbl 1408.35078 Bellomo, N.; Tao, Y.; Winkler, M. 3 2018 Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production. Zbl 1406.35068 Tao, Youshan; Winkler, Michael 94 2017 Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. Zbl 1516.35092 Tao, Youshan; Winkler, Michael 87 2017 Boundedness in a parabolic-elliptic chemotaxis-growth system under a critical parameter condition. Zbl 1524.92020 Hu, Bingran; Tao, Youshan 34 2017 Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model. Zbl 1372.35038 Lou, Yuan; Tao, Youshan; Winkler, Michael 11 2017 Asymptotic behavior in a chemotaxis-growth system with nonlinear production of signals. Zbl 1360.35028 Tao, Youshan; Liu, Yuanyuan 6 2017 Dynamics in a parabolic-elliptic two-species population competition model with cross-diffusion for one species. Zbl 1480.92174 Liu, Yuanyuan; Tao, Youshan 2 2017 Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Zbl 1356.35054 Tao, Youshan; Winkler, Michael 109 2016 To the exclusion of blow-up in a three-dimensional chemotaxis-growth model with indirect attractant production. Zbl 1351.35076 Hu, Bingran; Tao, Y. 66 2016 Boundedness in a chemotaxis system with nonlinear signal production. Zbl 1374.35009 Liu, Dongmei; Tao, Youshan 52 2016 Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion. Zbl 1326.35407 Tao, Youshan; Tello, J. Ignacio 6 2016 Explicit lower bound of blow-up time in a fully parabolic chemotaxis system with nonlinear cross-diffusion. Zbl 1331.35167 Tao, Youshan; Vernier Piro, Stella 6 2016 Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Zbl 1326.35397 Bellomo, N.; Bellouquid, A.; Tao, Y.; Winkler, M. 645 2015 Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Zbl 1328.35084 Tao, Youshan; Winkler, Michael 152 2015 Large time behavior in a multidimensional chemotaxis-haptotaxis model with slow signal diffusion. Zbl 1328.35103 Tao, Youshan; Winkler, Michael 132 2015 Boundedness vs. blow-up in a two-species chemotaxis system with two chemicals. Zbl 1329.35075 Winkler, Michael; Tao, Youshan 78 2015 Global boundedness in a fully parabolic attraction-repulsion chemotaxis model. Zbl 1331.35174 Liu, Dongmei; Tao, Youshan 66 2015 Persistence of mass in a chemotaxis system with logistic source. Zbl 1321.35084 Tao, Youshan; Winkler, Michael 51 2015 Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant. Zbl 1295.35144 Tao, Youshan; Winkler, Michael 116 2014 Dominance of chemotaxis in a chemotaxis-haptotaxis model. Zbl 1293.35047 Tao, Youshan; Winkler, Michael 65 2014 Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model. Zbl 1312.35171 Tao, Youshan; Winkler, Michael 62 2014 Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. Zbl 1295.35098 Lou, Yuan; Tao, Youshan; Winkler, Michael 22 2014 A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy. Zbl 1303.35116 Tao, Youshan; Guo, Qian; Aihara, Kazuyuki 10 2014 Competing effects of attraction vs. repulsion in chemotaxis. Zbl 1403.35136 Tao, Youshan; Wang, Zhi-An 207 2013 Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Zbl 1283.35154 Tao, Youshan; Winkler, Michael 170 2013 Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension. Zbl 1272.35040 Tao, Youshan; Wang, Lihe; Wang, Zhi-An 54 2013 Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity. Zbl 1282.35189 Tao, Youshan 39 2013 Rogue wave management in an inhomogeneous nonlinear fibre with higher order effects. Zbl 1420.35357 He, J. S.; Tao, Y. S.; Porsezian, K.; Fokas, A. S. 14 2013 Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity. Zbl 1382.35127 Tao, Youshan; Winkler, Michael 499 2012 Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant. Zbl 1268.35016 Tao, Youshan; Winkler, Michael 228 2012 Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Zbl 1276.35105 Tao, Youshan; Winkler, Michael 148 2012 A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source. Zbl 1259.35210 Tao, Youshan; Winkler, Michael 156 2011 Boundedness in a chemotaxis model with oxygen consumption by bacteria. Zbl 1225.35118 Tao, Youshan 154 2011 Global existence for a haptotaxis model of cancer invasion with tissue remodeling. Zbl 1205.35144 Tao, Youshan 59 2011 Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis. Zbl 1195.35171 Tao, Youshan 112 2010 A density-dependent chemotaxis-haptotaxis system modeling cancer invasion. Zbl 1186.92026 Tao, Youshan; Cui, Chun 12 2010 A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor. Zbl 1196.35216 Tao, Youshan; Guo, Qian; Aihara, Kazuyuki 10 2010 Spin Hall effect associated with \(SU(2)\) gauge field. Zbl 1188.81101 Tao, Y. 1 2010 A combined chemotaxis-haptotaxis system: the role of logistic source. Zbl 1201.35005 Tao, Youshan; Wang, Mingjun 63 2009 Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source. Zbl 1160.92027 Tao, Youshan 55 2009 A free boundary problem modeling the cell cycle and cell movement in multicellular tumor spheroids. Zbl 1178.35387 Tao, Youshan 18 2009 A model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression. Zbl 1180.35584 Tao, Youshan; Guo, Qian; Aihara, Kazuyuki 9 2009 Parameter identification for a model of tumor growth in the presence of inhibitors. Zbl 1212.35516 Tao, Youshan; Bian, Baojun 2 2009 Global solution for a chemotactic-haptotactic model of cancer invasion. Zbl 1160.35431 Tao, Youshan; Wang, Mingjun 69 2008 Mathematical modeling of prostate tumor growth under intermittent androgen suppression with partial differential equations. Zbl 1165.92309 Guo, Qian; Tao, Youshan; Aihara, Kazuyuki 10 2008 Analysis of a chemotaxis model for multi-species host-parasitoid interactions. Zbl 1159.35376 Tang, Xifeng; Tao, Youshan 6 2008 A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus. Zbl 1115.35137 Tao, Youshan; Zhang, Hui 13 2007 Global solution to a model of tumor invasion. Zbl 1135.92020 Tao, Youshan; Zhu, Guo 13 2007 A free boundary problem modelling cancer radiovirotherapy. Zbl 1141.35476 Tao, Youshan; Guo, Qian 8 2007 An elliptic-hyperbolic free boundary problem modelling cancer therapy. Zbl 1105.35149 Tao, Youshan; Chen, Miaojun 23 2006 Analysis and simulation of a model for intracellular drug accumulation in tumors. Zbl 1089.92027 Tao, Youshan; Guo, Qian 1 2006 The competitive dynamics between tumor cells, a replication-competent virus and an immune response. Zbl 1066.92035 Tao, Youshan; Guo, Qian 19 2005 Oscillation of nonlinear hyperbolic equations with distributed deviating arguments. Zbl 1107.35405 Tao, Youshan; Yoshida, Norio 2 2005 Nonlinear analysis of a model of vascular tumour growth and treatment. Zbl 1073.35215 Tao, Youshan; Yoshida, Norio; Guo, Qian 14 2004 Nonlinear stability of the Muskat problem with capillary pressure at the free boundary. Zbl 1028.35123 Friedman, Avner; Tao, Youshan 18 2003 Analysis of a model of a virus that replicates selectively in tumor cells. Zbl 1052.92027 Friedman, Avner; Tao, Youshan 17 2003 Existence, uniqueness and approximation of classical solutions to nonlinear two-point boundary value problems. Zbl 1011.34008 Tao, Youshan; Gao, Guozhu 3 2002 Identifying the volatility of underlying assets from option prices. Zbl 0997.91024 Jiang, Lishang; Tao, Youshan 59 2001 Parabolic approximation to variational problems with double obstacles. Zbl 0990.49012 Tao, Youshan; Gao, Guozhu 1 2001 Muskat problem with surface tension. Zbl 0884.35176 Hong, Jiaxing; Tao, Youshan; Yi, Fahuai 10 1997 Quasi-stationary Stefan problem as limit case of Mullins-Sekerka problem. Zbl 0883.35137 Yi, Fahuai; Tao, Youshan; Liu, Zuhan 4 1997 Classical solution of Verigin problem with surface tension. Zbl 0889.35055 Tao, Youshan 2 1997 A chemical diffusion process with reaction taking place at free boundary. Zbl 0906.35117 Ding, Shijin; Tao, Youshan; Yin, Hong-Ming 1 1997 Classical Verigin problem as a limit case of Verigin problem with surface tension at free boundary. Zbl 0859.35065 Tao, Youshan; Yi, Fahuai 2 1996 all cited Publications top 5 cited Publications all top 5 Cited by 1,423 Authors 122 Winkler, Michael 70 Tao, Youshan 67 Mu, Chunlai 53 Zheng, Jiashan 49 Zheng, Pan 40 Wang, Liangchen 39 Liu, Bin 39 Wang, Zhian 34 Yokota, Tomomi 32 Ren, Guoqiang 28 Wang, Yifu 28 Xiang, Zhaoyin 27 Jin, Haiyang 26 Lankeit, Johannes 26 Zheng, Sining 25 Elaiw, Ahmed M. 23 Lin, Ke 22 Shen, Wenxian 21 Viglialoro, Giuseppe 21 Xiang, Tian 20 Liu, Zuhan 19 Bellomo, Nicola 19 Wang, Wei 18 Mizukami, Masaaki 17 Deng, Zuicha 17 Hu, Xuegang 17 Wang, Yulan 17 Yang, Liu 16 Dai, Feng 16 Fuest, Mario 16 Liu, Ji 16 Zhou, Ling 15 Black, Tobias 15 Fujie, Kentaro 15 Jiang, Jie 15 Kang, Kyungkeun 15 Qiu, Shuyan 14 Guillén González, Francisco M. 14 Ke, Yuanyuan 14 Negreanu, Mihaela 14 Tu, Xinyu 13 Li, Zhongping 13 Liu, Zhengrong 13 Shangerganesh, Lingeshwaran 13 Wang, Jianping 13 Wang, Yilong 13 Zhang, Qian 13 Zhang, Qingshan 13 Zhao, Jie 13 Zhao, Kun 12 Cao, Xinru 12 Jin, Chunhua 12 Li, Xie 12 Wang, Qi 11 Balachandran, Krishnan 11 Guo, Qian 11 Li, Dan 11 Lyu, Wenbin 11 Pan, Xu 11 Surulescu, Christina 10 Guo, Shangjiang 10 Ishida, Sachiko 10 Salako, Rachidi Bolaji 10 Stinner, Christian 10 Tello, José Ignacio 9 Alshamrani, Noura H. 9 Chiyo, Yutaro 9 Cieślak, Tomasz 9 Ding, Mengyao 9 Li, Yuxiang 9 Shi, Junping 9 Villamizar-Roa, Elder Jesús 9 Xie, Li 8 Frassu, Silvia 8 Hobiny, Aatef D. 8 Lee, Jihoon 8 Lei, Yuzhu 8 Li, Jing 8 Lin, Zhigui 8 Liu, Changchun 8 Marras, Monica 8 Matioc, Bogdan-Vasile 8 Rodríguez-Bellido, Maria Angeles 8 Rueda-Gómez, Diego Armando 8 Tao, Xueyan 8 Wang, Jinfeng 8 Wang, Mingxin 8 Wu, Sainan 8 Xing, Jie 8 Yoon, Changwook 7 Ahn, Inkyung 7 Ahn, Jaewook 7 Aihara, Kazuyuki 7 Bellouquid, Abdelghani 7 Chouhad, Nadia 7 Heihoff, Frederic 7 Jia, Zhe 7 Li, Bin 7 Li, Chenglin 7 Li, Yan ...and 1,323 more Authors all top 5 Cited in 218 Serials 183 Journal of Differential Equations 138 Journal of Mathematical Analysis and Applications 112 Nonlinear Analysis. Real World Applications 112 Discrete and Continuous Dynamical Systems. Series B 102 ZAMP. Zeitschrift für angewandte Mathematik und Physik 92 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 51 Discrete and Continuous Dynamical Systems 38 Mathematical Methods in the Applied Sciences 38 Applied Mathematics Letters 35 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 34 Nonlinearity 32 Computers & Mathematics with Applications 29 Acta Applicandae Mathematicae 25 Applicable Analysis 23 Journal of Mathematical Physics 23 SIAM Journal on Mathematical Analysis 21 Communications on Pure and Applied Analysis 20 Calculus of Variations and Partial Differential Equations 19 Mathematical Biosciences and Engineering 19 Boundary Value Problems 19 Discrete and Continuous Dynamical Systems. 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Académie des Sciences, Paris 7 Chaos, Solitons and Fractals 7 Applied Mathematical Modelling 7 Communications in Partial Differential Equations 7 Electronic Journal of Differential Equations (EJDE) 7 Advances in Difference Equations 6 Applied Mathematics and Optimization 6 Mathematische Nachrichten 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Discrete Dynamics in Nature and Society 6 Advances in Nonlinear Analysis 6 AIMS Mathematics 5 Indiana University Mathematics Journal 5 Journal of Computational and Applied Mathematics 5 Journal of Functional Analysis 5 Mathematics and Computers in Simulation 5 Results in Mathematics 5 Journal of Inverse and Ill-Posed Problems 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Journal of Biological Dynamics 5 Evolution Equations and Control Theory 4 Studies in Applied Mathematics 4 Transactions of the American Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Physica D 4 Applied Mathematics. Series B (English Edition) 4 Acta Mathematica Sinica. English Series 4 Acta Mathematica Scientia. Series A. (Chinese Edition) 4 Journal of Applied Mathematics and Computing 4 Computational & Mathematical Methods in Medicine 4 Science China. Mathematics 4 Journal of Elliptic and Parabolic Equations 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational Physics 3 Physica A 3 Funkcialaj Ekvacioj. Serio Internacia 3 Journal of Optimization Theory and Applications 3 Chinese Annals of Mathematics. Series B 3 Mathematical and Computer Modelling 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Biological Systems 3 Qualitative Theory of Dynamical Systems 3 Mathematical Modelling and Analysis 3 Quantitative Finance 3 Advanced Nonlinear Studies 3 Multiscale Modeling & Simulation 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Kinetic and Related Models 3 Open Mathematics 2 Communications in Mathematical Physics 2 Inverse Problems 2 Mathematical Biosciences 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Bulletin of the London Mathematical Society 2 Czechoslovak Mathematical Journal 2 Kyungpook Mathematical Journal 2 Proceedings of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 SIAM Journal on Control and Optimization 2 SIAM Journal on Numerical Analysis 2 Acta Mathematicae Applicatae Sinica 2 Applied Numerical Mathematics ...and 118 more Serials all top 5 Cited in 32 Fields 1,607 Partial differential equations (35-XX) 1,471 Biology and other natural sciences (92-XX) 113 Fluid mechanics (76-XX) 105 Numerical analysis (65-XX) 48 Ordinary differential equations (34-XX) 42 Calculus of variations and optimal control; optimization (49-XX) 41 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 29 Dynamical systems and ergodic theory (37-XX) 23 Probability theory and stochastic processes (60-XX) 16 Statistical mechanics, structure of matter (82-XX) 12 Operator theory (47-XX) 12 Systems theory; control (93-XX) 8 Real functions (26-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Integral equations (45-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Difference and functional equations (39-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Statistics (62-XX) 4 Mechanics of deformable solids (74-XX) 3 General and overarching topics; collections (00-XX) 3 Functional analysis (46-XX) 2 Functions of a complex variable (30-XX) 2 Differential geometry (53-XX) 2 Operations research, mathematical programming (90-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year