Properties of solutions for a chemotaxis system. (English) Zbl 0892.92009

Allegretto, W.; Xie, H.; Yang, Shixin

J. Math. Biol. 35, No. 8, 949-966 (1997).

Summary: We investigate mathematically the system of equations proposed by M.A.J. Chaplain and A.M. Stuart [IMA J. Math. Appl. Med. Biol. 10, No. 3, 149-168 (1993; Zbl 0783.92019)], to describe the chemotactic response of endothelial cells under the angiogenesis stimulus. In particular, we characterize the steady state endothelial cell density function, and give conditions on the chemotactic parameter k and cell proliferation parameter b that ensure that migration/ proliferation either does or does not occur in steady state. The time dependent problem is also treated.

MSC:

92C50	Medical applications (general)
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35G20	Nonlinear higher-order PDEs
35G30	Boundary value problems for nonlinear higher-order PDEs

Keywords:

chemotaxis; endothelial; angiogenesis; parabolic system