A family of evolution equations with nonlinear diffusion, Verhulst growth, and global regulation: Exact time-dependent solutions

A family of evolution equations describing a power-law nonlinear diffusion process coupled with a local Verhulst-like growth dynamics, and incorporating a global regulation mechanism, is considered. These equations admit an interpretation in terms of population dynamics, and are related to the so-called conserved Fisher equation. Exact time-dependent solutions exhibiting a maximum nonextensive q-entropy shape are obtained.