Time periodic solutions for a sixth order nonlinear parabolic equation in two space dimensions. (English) Zbl 1284.35037
Summary: We study the time periodic solution of a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Based on Leray-Schauder’s fixed point theorem and Campanato spaces, we prove the existence of time-periodic solutions in two space dimensions.
MSC:
| 35B10 | Periodic solutions to PDEs |
| 35K35 | Initial-boundary value problems for higher-order parabolic equations |
| 35K55 | Nonlinear parabolic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
Keywords:
sixth order parabolic; time-periodic solution; existence; oil-water-surfactant mixtures; Leray-Schauder’s fixed point theorem; Campanato spacesReferences:
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