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Mathematics
On an initial-boundary value problem arising in the dynamics
D. O. Tsvetkov Crimean Federal University, Taurida Academy,
Simferopol, Russia
Abstract:
A linearized
problem of small motions of a system of layers of incompressible ideal stratified fluids
with a free surface, covered with the elastic ice that is modeled by the elastic
plate, is considered.
With using the method of
the orthogonal projecting the boundary conditions on the moving
surface, the original
initial-boundary value problem is reduced to the equivalent Cauchy
problem for an ordinary differential equation of the second order in some
Hilbert space. We find the conditions under which there exists a time-strong solution to the initial-boundary value problem describing the evolution of the original hydrodynamics system.
Keywords:
stratified fluid, elastic ice, differential-operator
equation, the Cauchy problem in a Hilbert space, strong solution.
Received: 17.09.2018 Revised: 29.04.2019
Citation:
D. O. Tsvetkov, “On an initial-boundary value problem arising in the dynamics”, Chelyab. Fiz.-Mat. Zh., 4:2 (2019), 179–198
Linking options:
https://www.mathnet.ru/eng/chfmj137 https://www.mathnet.ru/eng/chfmj/v4/i2/p179
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Abstract page: | 143 | Full-text PDF : | 31 | References: | 22 |
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