Summary: On the asymptotic behavior of a system of
steepest descent equations coupled by a
vanishing mutual repulsion
and A. Cabot2
Departamento de Ingenier´ia Matem´atica and Centro de Modelamiento
Matem´atico, Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
Laboratoire LACO, Universit´e de Limoges, Limoges, France
Summary. We investigate the behavior at infinity of a special dissipative system,
which consists of two steepest descent equations coupled by a non-autonomous con-
servative repulsion. The repulsion term is parametrized in time by an asymptotically
vanishing factor. We show that under a simple slow parametrization assumption the
limit points, if any, must satisfy an optimality condition involving the repulsion
potential. Under some additional restrictive conditions, requiring in particular the
equilibrium set to be one-dimensional, we obtain an asymptotic convergence result.
Finally, some open problems are listed.