Partial Differential Equations and Its Application, Mathematical Biology; in particular, Free Boundary Problems, Chemotaxis-haptotaxis models, Chemotaxis-fluid models, Cancer models.
Youshan Tao, Michael Winkler: Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production, Journal of The European Mathematical Society, to appear.
Youshan Tao, Michael Winkler: Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system，Mathematical Models and Methods in Applied Sciences, to appear.
Yuanyuan Liu, Youshan Tao：Dynamics in a parabolic–elliptic two-species population competition model with cross-diffusion for one species，J. Math. Anal. Appl.，to appear.
Yuan Lou, Youshan Tao, Michael Winkler: Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model, J. Differential Equations 262 (2017), 5160-5178.
Yuanyuan Liu, Youshan Tao, Asymptotic behavior in a chemotaxis-growth system with nonlinear production of signals, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), 465-475
Bingran Hu, Youshan Tao, Boundedness in a parabolic–elliptic chemotaxis-growth system under a critical parameter condition, Appl. Math. Lett. 64 (2017), 1-7.
Bingran Hu, Youshan Tao, To the exclusion of blow-up in a three-dimensional chemotaxis-growth model with indirect attractant production, Mathematical Models and Methods in Applied Sciences 26 (2016), 2111-2128.
Youshan Tao, Michael Winkler: Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system, Z. Angew. Math. Phys. 67 (2016), Article 138.
Dongmei Liu, Youshan Tao: Boundedness in a chemotaxis system with nonlinear signal production, Appl. Math.-A JCU B 31 (2016), 379-388.
Youshan Tao, J. Ignacio Tello, Nonlinear Stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor, Mathematical Biosciences and Engineering 13 (2016), 193-207.
Youshan Tao, Stella V. Piro, Explicit lower bound of blow-up time in a fully parabolic chemotaxis system with nonlinear cross-diffusion, J. Math. Anal. Appl. 436 (2016), 16-28.
Youshan Tao, Michael Winkler: Large Time Behavior in a Multidimensional Chemotaxis-Haptotaxis Model with Slow Signal Diffusion, SIAM J. Math. Anal. 47 (2015), 4229-4250.
Youshan Tao, Michael Winkler: Persistence of mass in a chemotaxis system with logistic source, J. Differential Equations 259 (2015), 6142-6161.
Nicola Bellomo, Abdelghani Bellouquid, Youshan Tao, Michael Winkler: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues, Mathematical Models and Methods in Applied Sciences 25 (2015), 1663-1763.
Youshan Tao, Michael Winkler: Boundedness and decay enforced by quadratic degradation in a three-dimensioanl chemotaxis-fluid system, Z. Angew. Math. Phys. 66 (2015), 2555-2573.
Dongmei Liu, Youshan Tao: Global boundedness in a fully parabolic attraction-repulsion chemotaxis model, Math. Meth. Appl. Sci. 38 (2015), 2537-2546.
Youshan Tao; Qian Guo; Kazuyuki Aihara: A partial differential equation model for prostate tumor growth under intermittent homone therapy. J. Math. Biol. 69 (2014), 817-838.
Youshan Tao; Michael Winkler: Boundedness and stabilization in a multi-dimensional chemotaxis–haptotaxis model. Proc. Roy. Soc. Edinburgh Sect. 144 A (2014), 1067-1084.
Youshan Tao; Michael Winkler: Energy-type estimates and global solvability in a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant. J. Differential Equations 257 (2014), 784–815
Youshan Tao; Michael Winkler: Dominance of chemotaxis in a chemotaxis–haptotaxis model. Nonlinearity 27 (2014), no. 6, 1225-1239.
Yuan Lou; Youshan Tao; Michael Winkler: Approaching the ideal free distribution in two-species competition models with fitness-dependent dispersal. SIAM J. Math. Anal. 46 (2014), no.2, 1228-1262.
Youshan Tao; Michael Winkler: Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Ann. Inst. H. Poincare Anal. Non Lineaire 30 (2013), no. 1, 157-178.
Youshan Tao: Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity. Discrete Contin. Dyn. Syst. Ser. B 18 (2013), no. 10, 2705-2722.
Youshan Tao; Lihe Wang; Zhi-An Wang: Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension. Discrete Contin. Dyn. Syst. Ser. B 18 (2013), no. 3, 821-845.
Youshan Tao; Zhi-An Wang: Competing effects of attraction vs. repulsion in chemotaxis. Math. Models Methods Appl. Sci. 23 (2013), no. 1, 1-36.
Na Zhang; Youshan Tao:A free boundary problem modeling tumor growth with different chemotactic responses and random motions for various cell types.J. Math. Anal. Appl.398(2013),no. 2,534–541.
Youshan Tao and Michael Winkler: Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion, Discrete Contin. Dyn. Syst.-A 32 (2012), 1901-1914.
Youshan Tao and Michael Winkler, Eventual smoothness and stabilization of large-data solutions in three-dimensional chemotaxis system with consumption of chemoattractant, J. Differential Equations 252 (2012),2520-2543.
Youshan Tao and Michael Winkler: Boundedness in a quasilinear parabolic–parabolic Keller–Segel system with subcritical sensitivity, Journal of Differential Equations 252 (1) (2012), 692-715.
Youshan Tao, Boundness in a chemotaxis model with oxygen consumption by bacteria, J. Math. Anal. Appl. 381 (2011), 521-529,
Youshan Tao and Michael Winkler, A chemotaxis-haptotaxis model: the roles of nonlinear diffusion and logistic source, SIAM J. Math. Anal. 43 (2011), 685-704.
Youshan Tao, Global existence for a haptotaxis model of cancer invasion with tissue remodeling, Nonlinear Analysis Series B: Real World Applications 12 (2011), 418-435.
Youshan Tao and Chun Cui, A density-dependent chemotaxis-haptotaxis system modeling cancer invasion, J. Math. Anal. Appl. 367 (2010), 612-624.
Youshan Tao, Qian Guo and Kazuyuki Aihara, A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor, Journal of Nonlinear Sciences 20 (2010), 219-240.
Youshan Tao, Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis, Nonlinear Analysis Series B: Real World Applications 11 (2010), 2056-2064.
Youshan Tao and Mingjun Wang, A combined chemotaxis-haptotaxis system: The role of logistic source, SIAM J. Math. Anal. 41 (2009), 1533-1558.
Youshan Tao, Qian Guo and Kazuyuki Aihara, A model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression, Math. Models Methods Appl. Sci. 19 (2009), 2177-2201.
Youshan Tao, A free boundary problem modeling the cell cycle and cell movement in multicellular tumor spheroids, Journal of Differential Equations 247 (2009), 49-68.
Youshan Tao and Baojun Bian, Parameter identification for a model of tumor growth in presence of inhibitors, Acta Mathematical Scientia 29(A) (2009), 1175-1186. (in Chinese)
Youshan Tao, Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source, J. Math. Anal. Appl. 354 (2009), 60-69.
Qian Guo, Youshan Tao and Kazuyuki Aihara: Mathematical modelling of prostate tumor growth under intermittent androgen suppression with partial differential equations, International Journal of Bifurcation and Chaos 18 (2008), 3789-3797.
Youshan Tao and Qian Guo: A mathematical model of combined therapies against cancer using viruses and inhibitors, Sci. China Ser. A 51 (2008), 2315-2329.
Youshan Tao and Mingjun Wang: Global solution for a chemotactic-haptotactic model of cancer invasion, Nonlinearity 21 (2008), 2221-2238.
Xifeng Tang and Youshan Tao: Analysis of a chemotaxis model for multi-species host-parasitoid interactions, Appl. Math. Sci. 2 (2008), 1239-1252.
Youshan Tao and Guo Zhu: Global solution to a model of tumor invasion, Appl. Math. Sci. 1 (2007), 2385-2398.
Youshan Tao and Qian Guo: A free boundary problem modelling cancer radiovirotherapy, Math. Mod. Meth. Appl. Sci. 17 (2007), 1241-1259.
Youshan Tao and Hui Zhang: A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus, Math. Mod. Meth. Appl. Sci. 17 (2007), 63-80.
Youshan Tao and Norio Yoshida: Oscillation criteria for hyperbolic equations with distributed deviating arguments, Indian J. Pure and Appl. 37(5) (2006), 291-305.
Youshan Tao and Yan Yang: Analysis of a model of tumor invasion, Far J. Appl. Math. 24 (2006), 177-192.
Youshan Tao and Qian Guo: Simulation of a model of tumors with virus-therapy,International Series of Numerical Mathematics, Vol. 154 (2006), 435-444, Birkh user Verlag Basel/Switzerland.
Youshan Tao and Miaojun Chen: An elliptic-hyperbolic free boundary problem modelling cancer therapy, Nonlinearity 19 (2006), 419-440.
Youshan Tao and Qian Guo: Analysis and simulation of a model for intracellular drug accumulation in tumors, Applied Mathematics and Computation 176 (2006), 577-593.
Youshan Tao: Mathematical analysis of a model of a replication-competent virus in tumor cells, Acta Mathematical Scientia (Ser. A) 26 (2006), 183-199. (in Chinese)
Youshan Tao and Norio Yoshida: Oscillation of nonlinear hyperbolic equations with distributed deviating arguments, Toyama Math. J. 28 (2005), 27-40.
Youshan Tao and Qian Guo: The competitive dynamics between tumor cells, a replication-competent virus and an immune response, J. Math. Biology 51(2005), 37-74.
Youshan Tao, Norio Yoshida and Qian Guo: Nonlinear analysis of a model of vascular tumor growth and treatment, Nonlinearity 17 (2004), 867-895.
Avner Friedman and Youshan Tao: Analysis of a model of a virus that replicates selectively in tumor cells. J. Math. Biology 47(2003), 391-423.
Avner Friedman and Youshan Tao: Nonlinear stability of the Muskat problem with capillary pressure at the free boundary, Nonlinear Analysis 53(2003),45-80.
Youshan Tao and Guozhu Gao: Existence,uniqueness and approximation of classical solutions to nonlinear two-point boundary?value problems, Nonlinear Analysis 50 (2002),981-994.
Youshan Tao and Jizhou Zhang:A shooting method for the Swift-Hohennberg equation, Appl. Math.--J.Chinese Univ. Ser.B, 2002, 17(4):391-403.
Lishang Jiang and Youshan Tao:Identifying the volatility of underlying assets from option prices, Inverse Problems 17 (2001),137-155.
Youshan Tao and Guozhu Gao: Parabolic approximation to variational problems with double obstacles, J. Math. Anal. Appl. 259 (2001),650-659.
Youshan Tao and Guozhu Gao: Oscillation for forced odd order neutral differential equations, Appl.Math.--J. Chinese Univ. Ser.B 16(2001),133-140.
Youshan Tao and Guozhu Gao: Oscillation of forced neutral differential equations with positive and negative coefficients, Appl. Math.--J. Chinese Univ. Ser.B 13(1998), 271-280.
Youshan Tao: The Cauchy problem for some nonlinear hyperbolic equation of first order, [Chinese] J. Math. [Wuhan] 18 (1998), no.4,411-414.
Youshan Tao and Guozhu Gao: Asymptotic behavior of solutions for neutral differential equations with several delay arguments and positive-negative?coefficients, [Chinese] Acta Math. Sci. [Chinese]18 (1998)(Increased ssue), 119-124.
Shijin Ding, Youshan Tao and Hong-Ming Yin: A chemical diffusion process with?reaction taking place at free boundary, Canad. Appl. Math. Quart. 5(1997), 49-74.
Fahuai Yi, Youshan Tao and Zuhan Liu: Quasi-stationary Stefan problem as limit case of Mullins-Sekerka problem, Sci. China Ser. A 40 (1997),151-162.
Youshan Tao: Classical solution of Verigin problem with surface tension, Chinese Ann. Math. Ser. B 18 (1997), 393-404.
Jiaxing Hong, Youshan Tao and Fahuai Yi: Muskat problem with surface?tension, J. Partial Differential Equations 10 (1997), 213-231.
Youshan Tao and Fahuai Yi: Classical Verigin problem as a limit case of Verigin problem with surface tension at free boundary, Appl. Math.--J. Chinese Univ. Ser.B 11 (1996), 307-322.
Youshan Tao: The limit of the Stefan problem with surface tension and kinetic undercooling on free boundary, J. Partial Differential Equations 9 (1996),153-168.
Lishang Jiang, Youshan Tao and Fahuai Yi: On Muskat Problem, Variational problems and related topics [Japanese] [Kyoto,1995],No.951 (1996),28-39.
Youshan Tao: The Goursat problem for a semilinear wave equation in two- dimensional space, [Chinese] Acta Math. Sci. [Chinese]15 (1995), no.2,168- 171.
Youshan Tao, Initial-boundary value problems for second-order quasilinearhyperbolic equations with characteristic boundary, [Chinese] J. Math. Res. Exposition 14 (1994), no.3, 443-448.