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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.

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
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