We study the homogeneous Neumann initial-boundary value problem for the fully parabolic problem introduced by Anderson system in Mathematical modeling of dynamic adaptive of tumour angiogenesis, Journal of Theoretical Biology, 241 (2006), 564-589.According to Yagi's arguments in Abstract Parabolic Evolution equations, Springer Monographs in Mathematics, (2009), we reduce them to corresponding evolution equations and show the existence of time global solutions.
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