The asymptotics for $t\to\infty$ of the solution of the problem of the collapse of the intrusion spot in a viscous stratified fluid

We consider a linear system of partial differential equations that models, in the Boussinesq approximation, a vertical section of a viscous stratified fluid. We give formulations and short proofs of results on the asymptotic behavior as $t\to\infty$ of the solution of the Cauchy problem with discontinuous initial conditions.