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arXiv · 2510.10829

Existence and numerical approximation of a one-dimensional Boussinesq system with variable coefficients on a finite interval

Juan Carlos Muñoz Grajales·Deissy Marcela Pizo
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Abstract

In this paper, we investigate the well-posedness of a nonlinear dispersive model with variable coefficients that describes the evolution of surface waves propagating through a one-dimensional shallow water channel of finite length with irregular bottom topography. To complement the theoretical analysis, we utilize the numerical solver developed by the authors in \cite{PizoMunoz} to approximate solutions of the model on a finite spatial interval, considering various parameter values and forms of the variable coefficients in the Boussinesq system under study. Additionally, we present preliminary numerical experiments addressing an inverse problem: the reconstruction of the initial wave elevation and fluid velocity from measurements taken at a final time. This is achieved by formulating an optimization problem in which the initial conditions are estimated as minimizers of a functional that quantifies the discrepancy between the observed final state and the numerical solution evolved from a trial initial state.

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Juan Carlos Muñoz Grajales, Deissy Marcela Pizo. 2025-10-12. Existence and numerical approximation of a one-dimensional Boussinesq system with variable coefficients on a finite interval. https://arxiv.org/abs/2510.10829

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