Time-periodic boundary layer solutions to singularly perturbed parabolic problems
| Autor: | N. N. Nefedov, Oleh E. Omel’chenko, Lutz Recke, Valentin Fedorovich Butuzov |
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| Rok vydání: | 2017 |
| Předmět: |
Singular perturbation
Applied Mathematics 010102 general mathematics Mathematical analysis Monotonic function Fixed point 01 natural sciences Implicit function theorem 010101 applied mathematics Boundary layer Uniqueness 0101 mathematics Analysis Mathematics Sign (mathematics) Variable (mathematics) |
| Zdroj: | Journal of Differential Equations. 262:4823-4862 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2016.12.020 |
| Popis: | In this paper, we present a result of implicit function theorem type, which was designed for applications 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. |
| Databáze: | OpenAIRE |
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