Iskenderov, B. A.; Mamedov, D. Yu.; Sulejmanov, S. E. Mixed problem for the equation governing inertia-gravity waves in the Boussinesq approximation in a unbounded cylindrical domain. (Russian, English) Zbl 1177.76048 Zh. Vychisl. Mat. Mat. Fiz. 49, No. 9, 1659-1675 (2009); translation in Comput. Math., Math. Phys. 49, No. 9, 1583-1600 (2009). Summary: The unique solvability of an initial-boundary value problem for the equation governing inertia-gravity waves in the Boussinesq approximation in an unbounded multidimensional cylindrical domain is studied. The existence and uniqueness of a weak solution is proved, and its asymptotic behavior at long times is analyzed. The proofs are based on the Green’s function constructed in explicit form for the corresponding stationary problem. Cited in 1 Document MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:equations of inertia-gravity waves; Boussinesq approximation; unique solvability; asymptotic behavior of solutions; Green’s function method PDFBibTeX XMLCite \textit{B. A. Iskenderov} et al., Zh. Vychisl. Mat. Mat. Fiz. 49, No. 9, 1659--1675 (2009; Zbl 1177.76048); translation in Comput. Math., Math. Phys. 49, No. 9, 1583--1600 (2009) Full Text: DOI