A qualitative analysis of some models of tissue growth
The authors apply standard maximum principles to a general nonlinear parabolic partial differential equation describing the concentration of the growth inhibitory factor that controls cell mitosis. They show in this way that many of the qualitative features of the solution, which have been obtained from analytical solutions under special conditions on the cell geometry and depletion and source functions, can be obtained in general. They also discuss the applicability of this approach to the inverse problem of describing the source function from the solution.
general nonlinear parabolic partial differential equation
scientific article; zbMATH DE number 219757
scientific article