Analysis of a Nonlinear Parabolic Equation Modeling Phytoplankton Aggregation

ABSTRACT We prove the existence and uniqueness of a nonnegative global strong solution for a mathematical model of phytoplankton aggregation. This model consists in a diffusion equation with a nonlocal and nonlinear term responsible of self‐attraction of phytoplankton cells and a source term taking into account their demographic process. For the source term, we consider first a linear growth and then a nonlinear one. The main difficulty in solving this partial differential equation lies in the nonlocal term modelling interaction between phytoplankton cells. We propose to use energy inequality to reduce the problem to the form for an appropriate operator . The latter will be solved by a fixed point procedure where the calculations are facilitated by the energy inequality. We finish the manuscript by studying the stationary problem for both forms of the source term.