On some anisotropic, nonlocal, parabolic singular perturbations problems

Abstract

This article is devoted to the study of the anisotropic singular perturbations theory for some quasilinear parabolic problems. Describing the asymptotic behaviour of the solutions of nonlocal problems yields to show the existence of solution to some integro-differential problems. The closeness between the solutions of these two kinds of problems is established.

Keywords:

• parabolic problems
• anisotropic singular perturbations
• asymptotic behaviour

AMS Subject Classifications:

• 35B25
• 35B40
• 35L15
• 35L20
• 35L70

Acknowledgements

The authors are grateful to the Swiss National Science Foundation for the support under the contracts #20 − 113287/1 and #20 − 117614/1.