Existence and numerical approximation of a one-dimensional Boussinesq system with variable coefficients on a finite interval
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914089658220544 |
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| author | Grajales, Juan Carlos Muñoz Pizo, Deissy Marcela |
| author_facet | Grajales, Juan Carlos Muñoz Pizo, Deissy Marcela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and numerical approximation of a one-dimensional Boussinesq system with variable coefficients on a finite interval Grajales, Juan Carlos Muñoz Pizo, Deissy Marcela Numerical Analysis Analysis of PDEs 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. |
| title | Existence and numerical approximation of a one-dimensional Boussinesq system with variable coefficients on a finite interval |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2510.10829 |