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

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
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