Time-periodic boundary layer solutions to singularly perturbed parabolic problems
- Omel'chenko, Oleh
- Recke, Lutz
- Butuzov, Valentin
- Nefedov, Nikolay
2010 Mathematics Subject Classification
- 35B25 35B10 35K20 35K58
- Monotone and non-monotone boundary layers, two independent singular perturbation parameters, periodic-parabolic boundary value problem, implicit function theorem
In this paper, we present a result of implicit function theorem type, which was designed for application to singularly perturbed problems. This result is based on fixed point iterations for contractive mappings, in particular, no monotonicity or sign preservation properties are needed. Then we apply our abstract result to time-periodic boundary layer solutions (which are allowed to be non-monotone with respect to the space variable) in semilinear parabolic problems with two independent singular perturbation parameters. We prove existence and local uniqueness of those solutions, and estimate their distance to certain approximate solutions.
- J. Differential Equations, 262 (2017) pp. 4823--4862.