A COMBINED CHEMOTAXIS-HAPTOTAXIS SYSTEM: THE ROLE OF LOGISTIC SOURCE

作者：Tao Youshan^*; Wang Mingjun

来源：SIAM Journal on Mathematical Analysis, 2009, 41(4): 1533-1558.

DOI：10.1137/090751542

• chemotaxis-haptotaxis
• logistic source
• global existence
• uniform boundedness
• cancer invasion model

This paper deals with a 3 x 3 chemotaxis-haptotaxis system modeling cancer invasion. The model consists of a parabolic chemotaxis-haptotaxis partial differential equation (PDE) describing the evolution of tumor cell density, an elliptic PDE governing the evolution of proteolytic enzyme concentration, and an ordinary differential equation (ODE) modeling the proteolysis of extracellular matrix. In three space dimensions, the existence, uniqueness, and uniform-in-time boundedness of global classical solutions to the above system is proved for large mu > 0 by raising the a priori estimate of a solution from L(1)(Omega) to L(2)(Omega) and then to L(4)(Omega); in two space dimensions, the existence, uniqueness, and boundedness is proved for any mu > 0 by raising the a priori estimate of a solution in the following way: L(1)(Omega) -> L(3)(Q(T)) -> L(2)(Omega) -> L(4)(Q(T)) -> L(3)(Omega). The above-mentioned mu is the logistic growth rate of cancer cells, Omega subset of R(d) (d = 2 or 3) is a bounded domain, and Q(T) = Omega x (0, T). The central point of this paper is to develop new L(p)-estimate techniques for a 3 x 3 chemotaxis-haptotaxis system.

• 出版日期2009
• 单位东华大学