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arXiv · 2009.09532

The Linearized Classical Boussinesq System on the Half-Line

C. M. Johnston·Clarence T. Gartman·Dionyssios Mantzavinos
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Abstract

The linearization of the classical Boussinesq system is solved explicitly in the case of nonzero boundary conditions on the half-line. The analysis relies on the unified transform method of Fokas and is performed in two different frameworks: (i) by exploiting the recently introduced extension of Fokas's method to systems of equations; (ii) by expressing the linearized classical Boussinesq system as a single, higher-order equation which is then solved via the usual version of the unified transform. The resulting formula provides a novel representation for the solution of the linearized classical Boussinesq system on the half-line. Moreover, thanks to the uniform convergence at the boundary, the novel formula is shown to satisfy the linearized classical Boussinesq system as well as the prescribed initial and boundary data via a direct calculation.

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C. M. Johnston, Clarence T. Gartman, Dionyssios Mantzavinos. 2020-09-20. The Linearized Classical Boussinesq System on the Half-Line. https://arxiv.org/abs/2009.09532

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