On a two species ecological system, structured on ages and involving diffusion (Q1084357)

The ecological system described in this paper is modeled by the partial differential equations system \[ \partial u_ i/\partial t+\partial u_ i/\partial a-A^ 2_ i\partial^ 2u_ i/\partial x^ 2=\lambda_ iu_ i,\quad b_ i(t,x)=\int^{\infty}_{0}\mu_ i(t,a,x)u(t,a,x)da, \] \[ u_ i(0,a,x)=u_{i0}(a,x),\quad i=1,2, \] where \(u_ i\) are the densities of the populations, \(b_ i\) their offspring densities, \(\mu_ i\) the birth rate and \(\lambda_ i\) the death rate of population i, the last one depending on the point x, the time and a functional which depends on the density of the species j(j\(\neq i).\) Existence and uniqueness theorems are proved, as well as some asymptotical properties and the dependence of the solution on the initial data.