Abstract:
In this paper we study initial-boundary value problems on a half-strip with different types of boundary conditions for the generalized two-dimensional Kawahara equation with nonlinearity of higher order. The solutions are considered in weighted at infinity Sobolev spaces. The use of weighted spaces is crucial for the study. We establish results on global existence and uniqueness in classes of weak and strong solutions, as well as large-time decay of week and strong solutions under small input data. Acknowledgements The work was supported by the Ministry of Science and Higher Education of Russian Federation: agreement no 075-03-2020-223/3 (FSSF-2020-0018).
Keywords:two-Dimensional kawahara equation, solvability of the initial bundary value problem, dissipation of solutions at infinity.
