Nonnegative solutions to an integral equation and its applications to systems of boundary value problems.
This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.
We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...