[1] Smoller J. Shock Waves and Reaction Diffusion Equations. Grundlehren Series 258. Springer-Verlag, 1982
[2] Qin Y, Li H. Global existence and exponential stability of solutions to the quasilinear thermo-diffusion equations with second sound. Acta Mathematica Scientia, 2014, 34B(3):759-778
[3] Wang S L, Feng X L, He Y N. Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence. Acta Mathematica Scientia, 2011, 31B(5):1959-1967
[4] Jin Z, Ma Z E, Han M A. Global stability of an SIRS epidemic model with delays. Acta Mathematica Scientia, 2006, 26B(2):291306
[5] Li W T, Wang Y, Zhang J F. Stability of positive stationary solutions to a spatially heterogeneous coop-erative system with cross-diffusion. Elec J Differ Equ, 2012, 223:1-18
[6] Yu X, Sun F. Global dynamics of a predator-prey model incorporating a constant prey refuge. Elec J Differ Equ, 2013, 04:1-8
[7] Baurmann M, Gross T, Feudel U. Instabilities in spatially extended predator prey systems:Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. J Theor Biol, 2007, 245:220-229
[8] Ainseba B E, Bendahmane M, Noussair A. A reaction-diffusion system modeling predator-prey with prey-taxis. Nonlinear Anal Real World Appl, 2008, 9:2086-2105
[9] Tao Y, Cui C. A density-dependent chemotaxis-haptotaxis system modeling cancer invasion. J Math Anal Appl, 2010, 367:612-624
[10] Patlak C S. Random walk with persistence and external bias. J Theor Biol, 1971, 30:235-248
[11] Keller E F, Segel L A. Initiation of of slide mold aggregation viewed as an instability. J Theor Biol, 1970, 26:399-415
[12] Keller E F, Segel L A. Traveling bands of chemotactic bacteria:a theoretical analysis. J Theor Biol, 1971, 30:235-248
[13] Keller E F. Assessing the Keller-Segel model:how has it fared//Biological Growth and Spread. Lect Notes Biom, 38.(Proc Conf Heidelberg, 1979). Springer-Verlag, 1980:379-387
[14] Cieslak T, Morales-Rodrigo C. Quasilinear nonlinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect:existence and uniqueness of global-in-time solutions. Topol Methods Nonlinear Anal, 2007, 29:361-382
[15] Hillen T, Painter K. Global existence for a parabolic chemotaxis model with prevention of overcrowding. Adv Appl Math, 2001, 26:280-301
[16] Kowalczyk R, Szymaska Z. On the global existence of solutions to an aggregation model. J Math Anal Appl, 1971, 30:235-248
[17] Tao Y. Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source. J Math Anal Appl, 2009, 354:60-69
[18] Tello J T, Winkler M. A chemotaxis system with logistic source. Comm Partial Differential Equations, 2007, 32:849-877
[19] Li C, Wang X, Shao Y. Steady states of a predator-prey model with prey-taxis. Nonlinear Anal, 2014, 97:155-168
[20] Ladyzenskaja O A, Solonnikov V A, Ural'ceva N N. Linear and Quasi-Linear Equations of Parabolic Type. Amer Math Soc Transl 23. Providence, RI:Amer Math Soc, 1968
[21] LaSalle J, Leftschetz S. Stability by Lyapunov's Direct Method. New York:Academic Press, 1961 |