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Displaying 141 –
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The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution.
Evolution equations featuring nonlinearity, dispersion and
dissipation are considered here. For classes of such equations
that include the Korteweg-de Vries-Burgers equation and the
BBM-Burgers equation, the zero dissipation limit is studied.
Uniform bounds independent of the dissipation coefficient are derived
and zero dissipation limit results with
optimal convergence rates are established.
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