Exponential asymptotic stability via Krein--Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems
- Nefedov, Nikolai N.
- Recke, Lutz
- Schneider, Klaus R.
2010 Mathematics Subject Classification
- 35B25 35B10 35B35 35K10 35K90
- singularly perturbed parabolic Dirichlet problems, exponential asymptotic stability, Krein-Rutman theorem, lower and upper solutions
We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein-Rutman theorem.