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On the asymptotic behavior of a system of steepest descent equations coupled by a
 

Summary: On the asymptotic behavior of a system of
steepest descent equations coupled by a
vanishing mutual repulsion
F. Alvarez1
and A. Cabot2
1
Departamento de Ingenier´ia Matem´atica and Centro de Modelamiento
Matem´atico, Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
falvarez@dim.uchile.cl
2
Laboratoire LACO, Universit´e de Limoges, Limoges, France
alexandre.cabot@unilim.fr
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.

  

Source: Alvarez, Felipe - Departamento de Ingeniería Matemática, Universidad de Chile

 

Collections: Mathematics; Engineering