Study of a variational inequality with a singular perturbation term

Abstract

A study of the asymptotic behaviour of a degenerate singular perturbation problem for a class of variational inequalities depending on a small positive parameter is introduced. An existence and uniqueness result for nonlinear problems with boundary terms, modelling the growth of bacteria populations, is also given.

Keywords:

• variational inequality
• asymptotic convergence
• singular perturbation
• population

2000 AMS Subject Classifications :

• Primary 47J20
• 35J85
• 35B25
• Secondary 92D25

Acknowledgements

The work by Álvarez-Dios has been finantially supported by the Spanish Ministerio de Educación y Ciencia (Consolider project ‘Aquagenomics: Mejora de la produccción en acuicultura mediante herramientas de biotecnología’ CSD200700002). Muñiz has been supported by MTM2008-02483.