# Controllability for a degenerate cascade system

## TL;DR

This paper investigates the null controllability of a degenerate cascade system modeling predator-prey interactions, using Carleman estimates to establish observability inequalities for the adjoint problem.

## Contribution

It introduces a novel controllability analysis for a degenerate, age-structured predator-prey system with boundary degeneracy, employing advanced Carleman estimates.

## Key findings

- Established null controllability under certain conditions.
- Derived new Carleman estimates for degenerate systems.
- Proved observability inequalities for the adjoint problem.

## Abstract

In this paper we consider a cascade system in non divergence form which models the interaction between two different species, the first one can be seen as a predator and the other as a prey. Both of them depend on time, on age and on space. Moreover, the diffusion coefficients degenerate at the boundary of domain. We study, in particular, null controllability of the system via the observability inequality for the non homogeneous adjoint problem, which is deduced by Carleman estimates.