Delayed exchange of stabilities in a class of singularly perturbed parabolic problems
- Nefedov, Nikolai N.
- Schneider, Klaus R.
2010 Mathematics Subject Classification
- 35B25 35K20
- Singularly perturbed parabolic problem, delayed exchange of stabilities, upper and lower solutions
We consider a class of singularly perturbed parabolic problems in case of exchange of stabilities, that is, the corresponding degenerate equation has two intersecting roots. By means of the technique of asymptotic lower and upper solutions we prove that the considered initial-boundary value problem has a unique solution exhibiting the phenomenon of delayed exchange of stabilities. Thus, the problem under consideration has a canard solution.