A model of proliferating cell populations with infinite cell cycle length: Semigroup existence
The paper is essentially devoted to studying the following partial differential equation \[ \frac{\partial f}{\partial t}=-\frac{\partial f}{\partial a}-\mu f \] with boundary condition \[ f(t,0,l)=[Kf(t,\cdot,\cdot)](l), \] where \(K\) is a linear operator on suitable trace spaces. The problem studied here comes from a mathematical model of an age structured cell population. The author shows that the problem is well-posed and gives the explicit expression of the generated semigroup under certain conditions on \(\mu\). A concrete example is given to illustrate the results.
scientific article; zbMATH DE number 5712200