We prove a weak maximum principle for structured population models with dynamic boundary conditions. We establish existence and positivity of solutions of these models and investigate the asymptotic behaviour of solutions. In particular, we analyse so called size profile.

Even though several methods of diffusion analysis avoid a necessity for the Matano plane determination, the Matano plane locations are of interest in the multicomponent couples and when tracer experiments are performed. The positions of the Matano plane calculated from the concentration profiles should be exactly the same. However, due to experimental errors, the results can differ significantly. In the paper we consider Matano...

We consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.