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Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom. (English. Russian original) Zbl 1418.76043

Differ. Equ. 54, No. 8, 1057-1072 (2018); translation from Differ. Uravn. 54, No. 8, 1075-1089 (2018).
The authors develop a method to solve the linearized shallow water equations for the piston model of tsunami, i.e., \(\eta_t=\langle\nabla,c(x)\nabla\rangle\eta\) with initial conditions \(\eta(0)\), \(\eta_t(0)\). First, they homogenize the problem (over uneven ocean bottom) to get a linear equation with sufficiently smooth coefficients. Then, they apply geometric optics approximation together with semiclassical approximation. Asymptotic solutions are compared with solutions obtained numerically in certain cases.

MSC:

76M50 Homogenization applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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