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- W4385374017 abstract "The large time $t$ asymptotics for scalar, constant coefficient,linear, third order, dispersive equations are obtained for asymptotically time-periodic Dirichlet boundary data and zero initial data on the half-line modeling a wavemaker acting upon an initially quiescent medium. The asymptotic Dirichlet-to-Neumann (D-N) map is constructed by expanding upon the recently developed $Q$-equation method. The D-N map is proven to be unique if and only if the radiation condition that selects the unique wavenumber branch of the dispersion relation for a sinusoidal, time-dependent boundary condition holds: (i) for frequencies in a finite interval, the wavenumber is real and corresponds to positive group velocity, (ii) for frequencies outside the interval, the wavenumber is complex with positive imaginary part. For fixed spatial location $x$, the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time-periodic wave. Uniform-in-$x$ asymptotic solutions for the physical cases of the linearized Korteweg-de Vries and Benjamin-Bona-Mahony (BBM) equations are obtained via integral asymptotics. The linearized BBM asymptotics are found to quantitatively agree with viscous core-annular fluid experiments." @default.
- W4385374017 created "2023-07-29" @default.
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- W4385374017 date "2023-07-27" @default.
- W4385374017 modified "2023-09-26" @default.
- W4385374017 title "Long-time asymptotics and the radiation condition for linear evolution equations on the half-line with time-periodic boundary conditions" @default.
- W4385374017 doi "https://doi.org/10.48550/arxiv.2307.14670" @default.
- W4385374017 hasPublicationYear "2023" @default.
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