Mathematical models of tumor growth systems. (Q2918598)

Systems of equations related to mathematical models of tumor growth are considered from the point of view of mathematical modelling as well as mathematical analysis. In particular, mean field approximation is discussed and a class of parabolic-ODE systems of the type NEWLINE\[NEWLINE q_t=\nabla \cdot (\nabla q - q\nabla \varphi (v)),\;v_t=q \text{ in }\Omega \times (0,T), NEWLINE\]NEWLINE NEWLINE\[NEWLINE \frac {\partial q}{\partial \nu }=0 \text{ on } \partial \Omega \times (0,T),\;q| _{t=0}=q_0,\;v| _{t=0}=v_0 \text{ in }\Omega NEWLINE\]NEWLINE are studied in a bounded domain \(\Omega \) in \(R^N\), \(\varphi \) being a smooth real function, \(q_0=q_0(x)>0\) and \(v_0=v_0(x)\) smooth initial conditions. A local and global existence results are formulated for the general and one-dimensional case, respectively.