Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom (Q1631169)

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.